Find an equation for the tangent to the curve at the given point. y = x^3/2 , (5, 62.5)?

I take it that this is (1/2) * x^3

y = (1/2) * x^3
y' = (3/2) * x^2
y' = (3/2) * 5^2 = (3/2) * 25 = 75/2

We need a line with a slope of 37.5 that passes through (5 , 62.5)

y - 62.5 = 37.5 * (x - 5)
2y - 125 = 75 * (x - 5)
2y - 125 = 75x - 375
2y = 75x - 250
y = 37.5 * x - 125...Show more