f(x) g(x) = x*f(x) and h(x) : * - 3

Q: For f(x) = x, the instantaneous rate of change is known to be 4 at x = 2. Find the equation of the…

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Q: f(3) = -9 and f'(3) = 7 . Then the equation of the tangent line to the graph of y = f(x) at x = 3 is

A: Given Data: The value of function at x=3 is: f(3)=-9 The value of the derivative of the function at…

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Q: Find all relative extrema of the function. Use the Second Derivative Test where applicable. (If an…

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Q: Right- and left-hand derivatives Let f (x) = |x|. (a) Calculate the right-hand derivatives of f(x)…

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Q: I. PROVING: Perform what is being asked 1. Prove whether the function h(x) is differentiable at x, =…

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A: Given  The equation is f(x) = x2 . The instantaneous rate of change is -6  at x=-3

Q: Using a Tangent Line The tangent line to the graph of y = g(x) at the point (4, 5) passes through…

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Q: Diffrentiation Formulas (derivative) Determine where, if anywhere, the tangent line to…

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Q: rection where the directional derivative is minimum for the function f(x,y) = xy+x²- (2,1).

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Q: Please show step-by-step solutions for the problems please!

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Q: Formula for slope: f(x + h) – f(x) m = lim h→0 h 1. Given the function: f(x) = x² + 2x + 1 where x =…

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A: We have to find relative extrema of the function: fx=x4-8x3+4 To find relative extrema first we need…

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Q: Tangent Line. If p(x) : 2x2 + 6х3 + + 4 (a) Then p'(1) = (b) The equation of the tangent line to the…

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Q: = -4 and g'(2) = 3. (Enter your answer as an equation in Find an equation of the tangent line to the…

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Q: Use the graph of a function y = f(x) to answer the questions about the derivative: the graphs…

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Q: Estimating changes with linear approximationsa. Approximate the change in y = ƒ(x) = x9 - 2x + 1…

A: a. Given: y=x9-2x+1 Differentiate the function: dydx=dx9-2x+1dxApply the Power Rule:…

Q: funchioN fo= x-2x-3 X+3 find the secod derivatve tx): Baseden: criical value -6.5, 0.5 and second…

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A: To show second derivative test is inconclusive.

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Q: lim X-1. x(e2x-1)

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Q: Tutorial Exercise Find the slope of the tangent line to the graph of the function at the given…

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Q: Find all relative extrema. Use the Second Derivative Test where applicable. (If an answer does not…

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Q: Suppose f(x) = 3,Va. (a) Find the slope of the function's graph at a = ¤ = 1. Slope = f'(1) = %3D…

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Q: ind the equation the tangent line and normal line to the graph of f(x) = x³ at x = 2.

A: Given f(x)=x3 substitute x=2 in f(x)⇒f(2)=23=8 The tangent line passes through the point (2,8)…

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Q: Find all relative extrema of the function. Use the Second-Derivative Test when applicable. (If an…

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Q: 75. Derivatives from tangent lines Suppose the line tangent to the graph of f at x = 2 is y = 4x + 1…

A: The line tangent to the graph of f at x=2 is y=4x+1.

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: