Question

Can someone help me on this question?

The line tangent to the graph of h(x) at x = 2 passes through the
points (0,4) and (6,13). Find h(2) and h'(2).

Answer 1

Alrighty then. The derivative of a function at x is the slope of the line tangent to the function at x. The tangent line has a slope of (13-4)/(6-0) = 9/6 = 1.5.
Thus, h'(2) = 1.5
Since we know the line passes through (0,4) and has a slope of 1.5, we know it will also pass through (2, 7). The tangent line at x will necessarily intersect the function at x. Thus, h(2) = 7.

Answer 2

Thanks !!