Find the slope of the tangent line to graph function at the given value of X?

Question

Help me. I don't understand how to do this problem. I've done one similar but with the fractional exponents I am not sure how to go about solving this. Please show me the steps.

y= -2X^1/2+X^3/2 ; X=9

? · Accepted Answer

You need to first differentiate y (wrt x)
So
dy/dx = -2(X^(-1/2)) * (1/2) + (3/2)X^(1/2)
= - X^(-1/2) +  (3/2)X^(1/2)

So for x = 9
dy/dx = -(9)^(-1/2) + (3/2) * 9^(1/2)
 = -1/3 + 9/2
= -25/6

Find the slope of the tangent line to graph function at the given value of X?

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