# Thread: slope and tangent lines

1. ## slope and tangent lines

Let

(a)Find the point(s) on the graph of f where the slope of the tangent line is equal to 0.

(b)Find the equation of the tangent line to the graph of f(x) at the point where x=0.

what method do I use to solve these problems and how do I solve them?

2. Originally Posted by Da Freak
Let

(a)Find the point(s) on the graph of f where the slope of the tangent line is equal to 0.

set f'(x) = 0 , solve for x, determine the function value(s) for each value of x

(b)Find the equation of the tangent line to the graph of f(x) at the point where x=0.

you need two things ... the point of tangency (0, f(0)) on the curve and the slope at that point, f'(0)

y - f(0) = f'(0)(x - 0)

what method do I use to solve these problems and how do I solve them?
...

3. Originally Posted by Da Freak
Let

(a)Find the point(s) on the graph of f where the slope of the tangent line is equal to 0.

(b)Find the equation of the tangent line to the graph of f(x) at the point where x=0.

what method do I use to solve these problems and how do I solve them?
(a) x-coordinate of points: Solve f'(x) = 0 for x.

y-coordinate of points: Substitute above values of x into y = f(x).

(b) The point has coordinates (0, -10) so (0, -10) is a known point on the tangent line.

Calculate gradient = m = f'(0).

So now you have a point and a gradient - if you're studying calculus you should certainly know how to get the equation of a line from these two things.