Question

hw 9 - the tangent line section 2.4: problem 5 (1 point)
let (f(x)=5x^{1.5}-3sqrt{x}+5).
(a) find (f(x)).
(f(x)=)
(b) find the slope of the line tangent to the graph of (f) at (x = 5).
slope at (x = 5:) (use at least 2 decimal places)
(c) find an equation of the line tangent to the graph of (f) at (x = 5).
tangent line: (y=)

Explanation:

Answer:

(a) \(7.5x^{0.5}-\frac{3}{2\sqrt{x}}\)
(b) \(6.09\)
(c) \(y - (5\times5^{1.5}-3\sqrt{5}+5)=6.09(x - 5)\) (or simplified further \(y=6.09x+(5\times5^{1.5}-3\sqrt{5}+5 - 30.45)\))