Question

If f(x) = mx² - 6x - 3 and f'(1) = 12. find the value of constant in (a) 9 (b) 3 (c)-3 (d) -4​

Answer 1

a) 186

b) 6

c) 42

Explanation:

`f(x) = m {x}^(2) - 6x - 3`

f'(1) = 12

f'(x) = 2mx - 6

12 = 2(1)m - 6

12 - 6 = 2m

`(2m)/(2) = (6)/(2)`

`m = 3`

`f(x) = 2 {x}^(2) - 6x - 3`

a)

f(9) = 3( 9)^2 - 6(9) - 3

f(9) = 186

b)

f( 3) = 3( 3)^2 - 6( 3) - 3

f(3) = 6

c)

f( - 3) = 3( - 3)^2 - 6( - 3) - 3

f(-3) = 42