Let f(x) = 2x - 2. (a) Use the limit process to find the slope of the line tangent to the graph of f at a = 2. Slope at a = 2: (b) Find an equation of the line tangent to the graph of f at a 2. Tangent line: y =

Q: Let f(x) = (x – 3)(5x + 7). Find an equation for the tangent line to the graph of f at x = 2.…

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Q: For the function ​f(x)=-3x^2 make a table of slopes of secant lines and make a conjecture about the…

A: It is known that the slope of a secant line between points (a, f(a)) and (b, f(b)) is given by:

Q: Find the slope of the curve y=x-3x-2 at the point P(2, -4) by finding the limit of the secant slopes…

A: (a) We have given,y=f(x)=x2−3x−2  →(i)P(2,−4) is a given point on the curve (i),Let h>0 be very…

Q: Find f(x) if f(0) = 0 and the tangent line at (x, ƒ (x)) has the slope x(x² + 2}°.

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Q: Find the slope-intercept equation of the tangent line to the graph of f(x) =√x at (1, 1).

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Q: -2 (a) Show that f'(x) using the definition of the derivative. (2x + 7)² (b) Find the equation of…

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Q: Find an equation of the tangent to the graph of y = f '(x) at x = −1 when f(x) = x3 + 6x2 + 2x.

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Q: Let f(x) = 6x2 Зх. (a) Find the instantaneous rate of change of f(x) at x = -1. (b) Find the slope…

A: Given the functionf(x)=6x2−3x

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

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Q: Use the limit definition of the derivative to find the slope of the tangent line to the curve f(x) =…

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Q: Use the limit definition to find the slope of the tangent line to the graph off at the given point.…

A: Given that ,  f(x) = 9x+9  at the point   (1,18) To find the slope of the tangent line to the graph…

Q: Let f(x) = 6 - 3x + 5x2. (a) Find f'(a) (b) What is the instantaneous rate of change of f when x =…

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Q: Let f(x) = (x - 12) / (2x + 6) Find an equation for the tangent line to the graph of f at x = 2 y =…

A: We find f'(x) first using quotient rule

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

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Q: Consider the function f(x) = x2 - 1. (a) Find f '(x) using the limit defination of the derivative.…

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Q: Given: f(x)=x2+2 find the equation of a line tangent at point P(1,3) using limits

A: To find the equation of a line tangent at point P(1,3) on below curve using limits.

Q: Find the equation of the line tangent to the graph of f(x)=−3cos(x) at x=−π3

A: As we know that: The first derivative of the function is equal to the slope of the tangent line to…

Q: For f(x)=x^4, the instantaneous rate of change is known to be -4 at x=-1. Find the equation of the…

A: Given that: *The function f(x) is f(x)=x4. *The instantaneous rate of change is the slope of the…

Q: 3. For f(x) = x -5x-6, make a table of slopes of secant lines and make a conjecture about the slope…

A: As we know that the slope of the tangent line is given by, dydxx=a=limh→0f(a+h)-f(a)h If a = 6, then…

Q: Show that the tangent line to the curve y = x3 at any point (a, a3) meets the curve again at a point…

A: Proof: The given curve is y=x3. Obtain the derivative of the function as follows: dydx=ddxx3…

Q: Find the derivative of the function by the limit process. g(t) = t³ +7t g'(t) =

A: We have to find derivative

Q: Let f(x) = 12 – x2 The slope of the tangent line to the graph of f(x) at - the point ( - 3, 3) is…

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Q: Find the derivative of the function by the limit process. g(t) = t³ + 6t g'(t) =

A: We can find the answer as below.

Q: on the chain rule find the tangent line to graph y=(x+2/x+1)^2, at x=0

A: We have to find tangent line to y , first we will find  value of y at x=0.

Q: find all points (x,y) on the graph of f(x)=3x^2-5x with tangent lines parallel to the line y=7x+1.

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Q: Find a function f such that f'(x) = r and the line 4r - y = 3 is tangent to the graph of f.

A: Given: f'(x)=x3Tangent line to the given curve is:  4x-12y=3Therefore: y=8x-6

Q: Let f(x) = 2x + 3 – 17e". Find the equation of the tangent line to the graph of f(x) at the point…

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Q: For the function f(x) =x2 , find the slope of the tangent line to the graph of f at the point (3, 9)…

A: For the function fx=x2, find the slope of the tangent line to the graph of f at the point (3, 9) on…

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Q: Let f(x) = /3x + 4. f(x) – f(a) Using the definition of derivative at a point, f'(a) = lim х — а…

A: The derivative of f at x = 1 is

Q: 8. For the function f(x) = x2 - 2, find: a) The slope of a tangent line at x = a.

A: To find the slope of tangent line at x=a.

Q: Find f(x) if f(2) = 3 and the tangent line at x has slope (x - 1)e - 2x, - 2x 3 fx) 2

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Q: Given the function, Show that it is not continuous at (3,-1) and determine the slope of the line…

A: The function will be discontinuous at 3, -1, if  either f(3,-1) is not defined, or,…

Q: (9) = ________________   Find an equation of the tangent line at  x = 9.

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Q: Consider the function (x) = -2r (a) Using the limit definition of the derivative, find f'(1). (b)…

A: (a). As we know that the expression for the derivative, according to the definition of limit is:…

Q: Compute f '(x) and find an equation of the tangent line to the graph at x = a. f (x) = x4, a = 2

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Q: Find the points on the graph of f(x) = where the tangent line is horizontal. x2+2

A: Given query is to find the points where tangent is horizontal.

Q: Let f(x) = 2x* + 3x° + 10. Find the equation of the line tangent line to the graph of Y point (1,…

A: Given  f(x) = 2X⁴ +3X³ +10 We need to find the equation of tangent of f(x) at the point (1,15)

Q: Suppose the curve y=f(x) has a tangent line y=4x-5 at x=1. Consider the function g(x)=2f(x)+x+1 What…

A: equation of tangent is y=4x-5 therefore equation of curve whose tangent is y=4x-5 ,…

Q: If f(x)  = 3x2 -x3, find f'(1) and use it to find an equationof the tangent line to the curve  y=…

A: Given that, y=fx=3x2-x3      ...(1)

Q: For f (x) = x 3, show that the slope of the secant line over [ -3, x] is x 2 - 3x + 9, and use this…

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Q: Estimate the slope of a line tangent to the curve f(x) = -2x2 + 3x +5 at point P(1, f(1))by doing…

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Q: Find the derivative of the function using the limit definition of derivative.  a. f(x) = 1/(x+3) b.…

A: Consider the given functions

Q: Find f(x) if f(0) = 8 and the tangent line at (x, f(x)) has slope 9x. %3D f(x) = %3D

A: Given:  f(0)=8 and the tangent line (x,f(x)) has slope 9x

Q: a) Give the limit definition for the derivative of f (x) b) Use the limit definition of the…

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Q: Suppose that f(x) = 5x - 2x. Use the limit definition of the derivative to find: (a) The slope of…

A: Given: y=f(x)=5x2-2x To find: the slope of the tangent line, the instantaneous rate of change and…

Q: Find the equation of the tangent to the curve y = 2x² – 1 at the point where z =1. Use the limit…

A: We know the standard form of tangent line is     --->     (y-y0) = m (x-x0)   where 'm' is the…

Q: For the function y= In(x² – 2) , the slope of the tangent at x = 2 is

A: