Question

Numerically estimate the slope of y = f(x) at r = a. 1. f(x) = x^2 - 2x, a = 2 2. f(x) = sin 2x, a = 0

Answer 1

Answer:

1. Slope at a=2 is 2.

2. Slope at a=0 is 2.

Step-by-step explanation:

We need to find the slope of y = f(x) at x = a.

1.

The given function is

$f(x)=x^2-2x$

It can be written as

$y=x^2-2x$

Differentiate with respect to x.

$y'=2x-2$

Substitute x=2 to find the slope of y = f(x) at a=2.

$y'=2(2)-2$

$y'=4-2$

$y'=2$

Therefore the slope of function at a=2 is 2.

2.

The given function is

$f(x)=\sin 2x$

It can be written as

$y=\sin 2x$

Differentiate with respect to x.

$y'=2\cos 2x$

Substitute x=0 to find the slope of y = f(x) at a=0.

$y'=2\cos 2(0)$

$y'=2(1)$

$y'=2$

Therefore the slope of function at a=0 is 2.