Find the slope and equation to the given function

Question

f(x)=5x x=4

(a) Use any method to estimate the slope of the tangent to the graph of the given function at the point with the given x-coordinate.

(b) Find an equation of the tangent line in part (a)

Answer 1

f(x) = 5 * sqrt(x)

= 5 * x^(1/2)

f'(x) = (5/2) x^(-1/2)

f(4) = 10 --> (4,10) is the tangent point

f'(4) = 5/4 --> is the slope at the tangent point

B = y - mx

= 10 - (5/4)(4) = 5 is the intercept

y = (5/4)x + 5