Question

Please help. I don't understand where to start with this one. If the slope of a strictly decreasing function at the point (a, b) is –4, what is the slope of the inverse of the function at the point (b, a)?
a. -1/4
b. –4
c. –1
d. The slope cannot be determined without knowing the equation of the function.

Answer 1

Answer:

a.$-\frac{1}{4}$

Step-by-step explanation:

We are given that

Slope of strictly decreasing function at the point (a,b) is -4.

We have to find the slope of the inverse of the function at the point (b,a).

Suppose , we have a function

$y=f(x)=-4x+2$

Slope of function f(x) at (x,y)=-4

$-4x=y-2$

$x=-\frac{1}{4}(y-2)$

Replace x by y and y by x.

$y=-\frac{1}{4}(x-2)$

Now, substitute $y=f^{-1}(x)$

$g(x)=f^{-1}(x)=-\frac{1}{4}(x-2)$

Differentiate w.r.t x

$g'(x)=\frac{-1}{4}$  Using rule ($\frac{dx^n}{dx}=nx^{n-1}$)

Slope of inverse of function f(x) at (y,x)=$-\frac{1}{4}$

Hence, the slope of inverse of the function at the point (b,a)is $-\frac{1}{4}$.

Option a is true.

Answer 2

Just assume the equation is y=-4x
to find the inverse you switch x and y so your equation becomes x=-4y, and then solve for y and you get, y=(-1/4)x so the slope is A)-1/4