For each of the given functions y = f(x). f(x) = 5, P(2, 1) (a) fınd the slope of the tangent line to its inverse function f ¯1 at the indicated point P. (b) fınd the equation of the tangent line to the graph of f -1 at the indicated point.

Q: After a recent flood the water level of a river is 43 feet, measurements show that it is receding at…

A: Given, W = fd = -3d +43  We have to find the formula for inverse function

Q: Find an equation of the tangent line to the graph of f at the given point. y = x³ - 2x + 1, (2,5) y…

A: We will find the required equation of tangent .

Q: Find an equation for the line tangent to the graph of 7x f(x) = x + 7 at the point (3, 2.1). y =

A: Given curve is Differentiating with respect to x, we get

Q: #1 Find the second derivative of each function 4x+2 a. a. f(x) Зх-6

A: First calculate 1st derivative of f(x) and g(t). Apply  d/dx of (u/v) in problem a. and chain rule…

Q: Differentiate the function. Then find an equation of the tangent line at the indicated point on the…

A:

Q: Consider the following function and point. =X+2, (3,5) (a) Find an equation of the tangent line to…

A: The given function .The aim is to find the equation of the tangent line at the point  and sketch its…

Q: Estimate the slope of the tangent line of the function y(x) = 24 at x = 1. 2+x (Use decimal…

A:

Q: Find the point(s) on the graph of f where the tangent line is horizontal. (If an answer does not…

A: Given- fx=xx2+49 To determine smaller x-value and larger x-value.

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: