function question?

Question

okay, so the function is f(x) = 3x^2 - 5x + k

a) write down f '(x)

The equation of the tangent to the graph of * f * at x=p is y=7x-9. Find the value of:

b) p

c) k

Answer 1

y'=6X-5

6p-5=7
6p=12

p=2

x=2
y=7*2-9=14-9=5

5=3*4-10+k
5-12+10=k

k=3

Answer 2

f '(x) = 6x - 5
So slope = 6p-5 = 7
Thus p = 2
When x = 2, y = 14-9 =5
So 5 = 3*(2)^2 - 5*2 +k
5 = 2 + k
k = 3