Find the slope of the tangent line of the function ﻿y left parenthesis x right parenthesis space equals space 4 x to the power of 3 divided by 2 end exponent minus 5 x to the power of 1 divided by 2 end exponent space comma space a t space x space equals space 16﻿

To find the slope of the tangent line to the function \( y(x) = \frac{4x^{3/2}}{2} - 5x^{1/2} \) at \( x = 16 \), we need to follow these steps:

### Step 1: Simplify the function
First, simplify the expression for \( y(x) \):
\[
y(x) = 2x^{3/2} - 5x^{1/2}
\]
since \( \frac{4}{2} = 

Find the slope of the tangent line of the function y(x) = 4x^(3/2) / 2 - 5x^(1/2) at x = 16

This problem demonstrates how to find the slope of the tangent line for the function y(x) = 4x^(3/2) / 2 - 5x^(1/2) at x = 16. It involves using differentiation techniques, including the power rule, and is ideal for students in Grades 11-12.

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