Question

If an equation of the tangent line to the curve y = f (x) at the point where a = 5
is y = 10x − 2, find  f (5) and  f '(5).

If I have the equation of the tangent line, don't I have the derivative? If so, can I simply substitute x in 10x-2 and solve for f'(5)?

Also, if thats true, then can I use integration to turn 10x-2 into 5x^2 -2x and sub in 5 to solve for f(5)?

(b) If the tangent line to y = f (x) at (-5, -1) passes through the point (6, 8), find  f (-5) and  f '(-5).

I am not sure how to approach this question. Please explain how you do it

Answer 1

Can you show me some of your worK?

Answer 2

f'(5) means slope of the tangent at x=5.
So, f'(5)=10
AND,
Since the curve f(x) and the tangent intersects at the point of contact..
f(5)=10*5-2=48

Answer 3

Now, use the same concept to do question number (b)