The instantaneous slope of f(x) when f(x) is rational f(x) = compute the instantaneous slope at: (0, –3)

Q: Consider the two functions fz) = 5x +5 and g(x) = 5x² - 5. a. Determine the instantaneous rate of…

A: rate of change means differentiate with respect to x so differentiate it f'(x) = 10x g'(x) = 10x   a…

Q: On the interval –5 < x < 6, for how many values does f (x)(graphed below) have a derivative equal to…

A: Given:

Q: Given f(x)= (x^2)/(x^2-4) a) Find the derivative b) Find the critical points

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Q: 1. Determine the true error and relative true error when approximating the derivative of ƒ(x) = -x²…

A: solution is here

Q: Find the local maximum and minimum values of f using both the First and Second Derivative Tests. x²…

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Q: Find an equation for the tangent line to the graph of the given function at ( – 5,32). - f(x)=x² +7…

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

Q: Determine the point(s) at which the graph of f(x) =  -4x/square root of 2x-1   has a horizontal…

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Q: a. Find the average rate of change of f(x) = -3x³ + x -1 between [-1,0]. b. Find the Difference…

A: Since you have posted multiple subparts, as per our policy we will answer first three subparts.…

Q: (x2-1) (x²+1-x) Q4 / Find the equation of tangent line at x = 1, where f(x) x*-x3

A: A tangent line to curve is a line that just touches the curve only one point.

Q: 11 at x = 10 Find the derivative of f(x) = f' 10 |(Type an integer or a simplified fraction.) %3D

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Q: Let f(x) = 3x² - 2x. (a) Use the definition of derivative and the procedure given in this section to…

A: Given that: f(x)=3x2-2x

Q: 8. Determine the intervals where the function is increasing or decreasing. Find the local maxima and…

A: First derivative test

Q: 3 + 3x – 5 Find the local maximum by solving the derivative P'(x)=0, – 2x + -- %3D |

A: Given Find out local maximum

Q: Find the r-value for all relative extrema of f(x) using the first derivative test. 1+x +x? f(x) : x2…

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Q: Find the absolute extrema if they exist, as well as all values of x where they occur, for the…

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Q: Find the average rate of change of the function f(x) = x² - 2x + 3 between x = -2 and 2 = 4. Type an…

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Q: Example: Use the Secant method to estimate the root of f(x) = e-x-x. Start with initial estimates…

A: To use secant method to estimate the root of fx=e−x−x

Q: Find an equation of the tangent line to the graph of the function f through the point (x0, y0) not…

A: The given function is fx=x.

Q: Find an equation of the tangent line to the graph of the function f through the point (x0, y0) not…

A: We have to find  an equation of the tangent line to the graph of the function f through the point…

Q: 7 Let f(x) = 6+-. (a) Find f'(x). f'(x) = %3D (b) Find the slope of the tangent line at a = 5. Slope…

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Q: Find f(x) if f(2) - 2x 3 and the tangent line at x has slope (x – 1)e* %3D f(x) =

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Q: %3D Apply the Chain Rule to find the tangent line to f(x) = 4v2x- 6e2-*at x = 2

A: We want to find the tangent of the given function at x=2 We know that slope of the tangent at a…

Q: Find the slope and the equation of the tangent line to the graph of the function at the given value…

A:

Q: f(x+ Ax)-f(x) Us the definition of the derivative f'(x) = lim Ax-0 to find the equation of the line…

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Q: 1.Use the second sufficient condition for an inflection point (the third derivative test) to find…

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Q: A quadratic function f(x) = x + 3 x2 + 2 x + 3 has an inflectional tangent y = 3 x + 3 at (0,0).…

A: Given:- A quadratic function f(x) = x3+3x2+2x + 3 has an inflectional tangent y = 3x + 3 at (0, 0).…

Q: Let f(x) be defined by f(x) = 3x² + 5x + 2. Find the slope of the tangent line to the curve y = f(x)…

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Q: a)Use the second derivative test to determine whether the function has a local maximum or local…

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Q: f(x)-x^3-x+1, a tangent line is drawn to f at x= -1. Using the equation of the tangent line,…

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Q: 6. Find the values of at which the graph of f(x) = = 4x² - 3x + 2 has a tangent line parallel to the…

A: Follow the procedure given below.

Q: Find the inflection points of the function f(x) = x 2 ln x

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Q: Find the absolute extrema if they exist, as well as all values of x where they occur, for the…

A:

Q: ind derivative w.r.t.x: f(x)=x3 -x. Al

A: Given,         f(x)=x3-x

Q: f(x+h)- f(x) 4x3+9x+5 Using lim0 Find the slope of the tangent line y = Зx-8 h at x = -1.

A:

Q: Let f(x) = 9 – x² The slope of the tangent line to the graph of f(x) at the point (-3,0) is The…

A:

Q: Find the relative extrema of f(x) = 2+ 90r 5x using both first and second derivative tests. f(x) has…

A: We can find the relative extremum as below

Q: Consider the function y = -x3 + 3x² – 2. a) Find the critical points. b) Use the 2nd Derivative Test…

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Q: Find the local maximum value of f using both the First and Second Derivative Tests. (If an answer…

A: Given fx=x+5-x

Q: Let f(x) = 21 – x² The slope of the tangent line to the graph of f(x) || at the point (-4, 5) is The…

A:

Q: Find f′(x) and find the equation of the line tangent to the graph of f at x=2.   f(x)=3x/2^x

A: Given:fx=3x2x , x=2Equation of Tangent line:y-y1=mx-x1ddxuv=vdudx-udvdxv2

Q: 5 Let f(x) = 2+ - (a) Find f' (x). f' (x) = (b) Find the slope of the tangent line at x = 5. Slope =…

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Q: Using forward, backward, and central finite divided difference to find the first derivative of f(x)…

A: here we find the first derivative of the function f(x) = ex -2x2 +3x -1 at x = 0.6 and h = 0.2 by…

Q: using the de fini tion of first derivativg find the SlOpe of tange nt line to the g raPhof the…

A:

Q: 5. Let f(x) = 5x4 - -2+8√√x-3. (a) Find f'(x). (b) Find an equation for the tangent line to the…

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Q: Find the absolute maximum and minimum values of the function over the indicated interval, and…

A: Solution of given question is written in below steps.

Q: Find the average rate of change of the function f(x) = = læ + 0x + 8, on the interval x E [-2,0].…

A: Given:fx=x2+8  on the    interval -2,0Average rate of change of the functionAx=fb-fab-aa=-2 , b=0

Q: 6. Find all relative extrema of the function h(x) = -3x5 + 5x3 using the Second Derivative Test.…

A: Relative maxima and minima