Question

Find an equation of the tangent line to h(x) = f(x)g(x) at x = 1

Answer 1

\[y=[f'(1)g(1) + f(1)g'(1)](x-1) + f(1)g(1)\]

Answer 2

well you need the point of the curve which will be (1, h(1))

you need to find the slope... but 1st you need to differentiate the function using the product rule

h'(x) = f(x)g'(x) + g(x)f'(x)

the slope at x = 1 is found by substituting x = 1 into the 1st derivative(above)

h'(1) = f(1)g'(1) + g(1)f'(1)

now you have a slope h'(1) and point (1, h(1))

use the point slope formula to find the equation of the tangent.

Answer 3

ok

Answer 4

so i got y = g(1)f'(1) + f(1)x g'(1) - f(1) g'(1) + f(1)g(1) is it correct?

Answer 5

@campell_st ?

Answer 6

@campbell_st

Answer 7

@ingenuus did i get it right?

Answer 8

no the answer is above

Answer 9

okay

Answer 10

do you understand the equation y=m(x-a) +b ?

Answer 11

yes

Answer 12

what is the slope m in your case

Answer 13

1?

Answer 14

why is it 1?