Question

Let f(x) = x ^3. The equation of the tangent line to f(x) at x = 5 is y= .

Using this, we find our approximation for 4.8 ^3 is .

Answer 1

I'm so confused

Answer 2

first inver opperation

Answer 3

what do you mean sir?

Answer 4

im a girl

Answer 5

The equation of the tangent line to f(x) at x = a is

L(x) = f(a) + f '(a) * ( x - a )

Answer 6

there you go

Answer 7

f(x) = x^3
f ' (x) = 3x^2

Answer 8

f(5) = 5^3 = 125
f ' (5) = 3*5^2 = 75

Answer 9

L(x) = f(a) + f '(a) * ( x - a )
L(x) = 125 + 75 ( x - 5 )

Answer 10

now plug in x = 4.8
L(4.8) = 125 + 75 ( 4.8 - 5) = 110

this is very close to the exact answer of
4.8^3 = 110.592

Answer 11

thank you so much @perl