For f(x): 1 -x² + x + 2, find: a) the equation of the line that is tangent to the graph of f at the point where x = 2. b) the point (as an ordered pair) on the graph of f where the tangent line is horizontal.

Q: Given f(x)=−2x^2+4x+13, find f′(−4) using the definition of a derivative.

A: f'(a) = limh→0 f(a+h)-f(a)h.

Q: Find the slope of the secant line to the function f(x)=4x²- 3x, through point P, where x= - 1, and…

A: To find the slope of secant line PQ to  the function f(x)

Q: Graph the function f(x) = coordinates are -2,0, and 1. 2a? and draw the tangent lines to the graph…

A: Sketch the function.

Q: b) Use the definition of the derivative to find the derivative of f(x) = 4x³ + - at a = 1. 23

A: Given: fx=4x3+1x3; x=1 We know that ddxxn=nxn-1                                          ..1

Q: Find the equation of the tangent line to the graph of f(x) = -2(3x – 1)³ at . Show work or explain…

A:

Q: Find the equation of the tangent to the curve y= 3x' – 4x² +2x–10 at the points where the curve cuts…

A:

Q: For the function f(x)=2x^3-12x^2+20, Use the SECOND DERIVATIVE TEST to find the relative extrema.

A:

Q: Find the equation of the line that is tanget to f(x)= 1/x at the point (2,1/2).

A: We need to find the equation of the line that is tangent to f(x) = 1/x at the point (2,1/2).

Q: If f(x) = 2x2 + 10x + 6, find the equation of the line tangent at x = %3D -1.

A: Given, f(x) = 2x2 + 10x + 6 So, y = 2x2 + 10x+ 6 for finding the equation of line  we first find the…

Q: Find the equation of the tan gent line to the graph of the equation f(x) = 5x - 8x +12, at the point…

A: Here we are going to solve only one question and for the remaining question post the question again.…

Q: Find the indicated derivative using the definition f(x) = 2x4+3x3-2x+7: f'(0)

A: Differentiation is the rate of change in the value of the dependent variable with respect to the…

Q: Find the slope m of the tangent line to the graph of the function at the given point and determine…

A:

Q: If f(x) = 7x2 - x³, find f'(1) and use it to find an equation of the tangent line to the curve y =…

A:

Q: Use the definition of derivative to a) f(x) = x - 2r? b) f(- %3D

A:

Q: Find the slope of the tangent line to the curve - 2x2 + 3xy + 4y° 3 242 at the point (- 1, 4).

A: Given curve is -2x2+3xy+4y3=242. To find: Slope of the tangent line to the given curve at the point…

Q: For the function ​f(x)=−6x2​, make a table of slopes of secant lines and make a conjecture about…

A:

Q: Find f'(x) using the rules for finding derivatives 4x2 - 5x + 2 f(x) = 3x +7

A: We have to find

Q: Jx + 2x f(x)=- 7х — 4х? 8.

A:

Q: What is the length of the curve y = sqrt(4-x2) from x = -2 to x = 1?

A: y=4-x2 Differentiating with respect to x, we get dydx=124-x2·d4-x2dx   ∵dxdx=12x=124-x2·0-2x=-x4-x2

Q: Find f' (x) using the rules for finding derivatives 4x2 – 7x +1 f(x): 2x + 9 f'(x)=O

A: To find The derivative of f(x)

Q: for the function f(x)=11x^3-x, find the slope of secant line at interval [1, 1.01]

A: We have given a function f(x).

Q: At which x location on the graph of f(x) = -x² - 2x + 15 is the slope of the tangent 0?

A:

Q: 4x+1 b. g(x) 9х-2

A: Given : g(x)=4x+19x-2   To Find : Derivative of g(x) using definition   NOTE:If f(x)=uv  , where u…

Q: iven the function y=2x³-4x²+5,

A: Given, the function               y=2x3-4x2+5

Q: Find the two points where the curve x2 + xy + y2 = 7 crosses the x-axis, and show that the tangents…

A: To determine the x-intercept of the curve and slope of the tangent at the intercept.

Q: The slope of the oblique asymptote to the curve f(x) = x +11 corresponds to

A: folllow the procedure given below.

Q: Find the slope of the secant line between x=−1 and x=2 on the graph of the function f(x)=−3x3+4x2+2.

A:

Q: Find the derivative of the functionf(x)= 9x² + 4x +6, using the definition of the derivative,

A:

Q: If f(x) = 9x2 - x³, find f'(2) and use it to find an equation of the tangent line to the curve y =…

A:

Q: Given f(x) = Vx+ 8, find f' (-4) using the definition of a derivative. %3D Provide your answer…

A:

Q: Find the equation of the secant line on the graph of the function f(x)=7x2 between the points where…

A: take x=-1 . take x=5

Q: For the function f(x) = 8x^3-2x^2+2x, Find the equation of the tangent line at x = 2.

A: Please see the answer in Step 2

Q: Determine the points where the curve f(x) = 2x3 + 3x2 – 36x + 1 has a horizontal tangent. -

A:

Q: Find f'(x) using the rules for finding derivatives 4x2 - 7x +6 f(x) = 2x + 1

A:

Q: Given the function F(x)= 1/x2 - Use the definition of the derivative to find f'(2)

A:

Q: Find the equation of the line tangent to the graph of f(x) = x² + = - 9 at x = 7. y = help…

A:

Q: If f(x) = 8x2 - x3, find f'(2) and use it to find an equation of the tangent line to the curve y =…

A: The given function is f(x)=8x2-x3

Q: For the function f(x)= 3x² +2x–1, Find the equation of the line tangent to the curve at x = -1 2.

A:

Q: If (x) = 8x² - x, find f(1) and use it to find an equation of the tangent line to the curve y = 8x-…

A: First of all find derivative and slope

Q: Determine an equation for the tangent to the curve f(x) = 2x3 + 6x2 - 2  at x = -3

A: Given query is to find the equation of the tangent.

Q: Find the slope of the tangent line to the curve - 2x2 + 4ry – 3y - 63 at the point (3, 3).

A:

Q: Find the derivative of the function f(x) = x2 -8x +9 at the number a

A: The given equation is f(x)=x2-8x+9 The derivative of the function is the rate of the change in the…

Q: Given use the definition of the derivative to show that f(x) = 4x + 3x- 1 f' (x) = 8x + 3

A: f(x)=4x2+3x-1 Definition of derivative:…

Q: In the next exercise you have to equal the derivative to zero and then clear x or a y to subtract in…

A:

Q: For the​ function, find the points on the graph at which the tangent line is horizontal. If none​…

A: To locate the points on the graph where the tangent is parallel to the x -axis