Question

The slope of the tangent line to the graph of a function, h(t) is 7/2t

The function passes through the point (5,3)
Find h(4)

Answer 1

well, we can find an approximation to h(4) by assuming that the tangent line at (5,3) stays close to the curve. So, assuming that you meant the slope is 7/(2t), h'(5) = 7/10

The tangent line is thus

7-3 = 7/10 (x-5)

now, plug in x=4 to approximate h(4)

If you meant h'(t) = (7/2)t, then make the appropriate adjustment