Mathematics: 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

A. 1/8x +1/8x Step-by-step explanation:1/8x +1/8x =2/8x = 1/4x...

Numerically estimate the slope of y = f(x) at

juter92

05.01.2022

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.

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.

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.

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