Consider the function f (x) = 2x2 – 3x + 5. Construct the formula for the average rate of change function r = ARC, (x) and use algebra to sımplify your answer as much as possible. df Use the simplified formula from Part (a) to determine the formula for You must employ dx the definition of the derivative as a limit of average rate of change functions.

Q: Exercise To Try 13 Find using implicit differentiation, of 2x³ – xy³ = 3. NOTE: You will use product…

A:

Q: h) f(x) = Write your answer in simplified factored form. %3D

A:

Q: h(x) = (x − 3)º(5x² + 3x)²

A:

Q: b. f(x)=7x²e"

A:

Q: The equation that describes the volume of the conical shape RELATES the quantities : volume, radius…

A:

Q: Find the derivative y = (2x – a) (x² + e-")

A: We havey= (2x-x3)(x2 + e-x)

Q: (2) Define: F(x)=√(r² + 1). e³r+² dr. (a) Use the fundamental theorem (II) to find the derivative…

A: The given integral equation is:F(x)=∫x0 r2+1 ·e3r+2 dr

Q: Use the product rule to differentiate the function: y = 2x-3ln x & for the derivative found, find…

A:

Q: exfex=6x²8h

A:

Q: Differentiate the function L(x) = -6e"(cscx + 7cotx). Answer L'(x) =

A: Given Equation : L(x)=−6ex(csc(x)+7cot(x))   L'(x)= derivative of L(x)

Q: y = 2x² - 8x. Determine the slope of the tangent to the function at x = 2.

A: To find the derivative of the function y=2x2-8xusing first principles,we start by using the…

Q: Answer: f'(3) could equal

A: Since f(2) = 13 f(4) = = 12.25   Also f"(x) >0 , which means f is concave upward

Q: How do you find the derivative of the quotient of two functionsthat are differentiable at a point?

A: Given: Let f and g be two differentiable function at point x.

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: