Mathematics: Given the function h(x)=-x^2+8x+24, determine the average rate of change of the function over the interval 0 is less than or equal to x is less than or equal to 9

Given the function h(x)=-x^2+8x+24, determine - id28244524661, Daveandemily17

bchamp2005p5upqx

15.01.2022

Average rate of change =-2

Step-by-step explanation:

First derivative of function represents rate of change.

$\frac{d}{dx}hx=\frac{d}{dx}(-x^2+8x+24)\\\\=-2x+8\\$

Now find out rate of change at end points

$(\frac{dh}{dx})_{x=0}=-2\times 0+8=8\\\\\\(\frac{dh}{dx})_{x=9}=-2\times 9+8=-10$

average rate of changes = $\frac{First\ derivative\ at\ last\ point\ -first\ derivative\ at\ initial\ point }{last\ point-initial\ point}$

$=\frac{-10-8}{9-0}\\\\=\frac{-18}{9}\\\\=-2$

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nathaliapachon1254

30.05.2023

Step-by-step explanation:

Use triangle congruency:

BC=EC, AC=DC - Given

m∠DCE = m∠ACB because they are vertical angles

Therefore ΔABC ≅ ΔDEC because of Side-Angle-Side congruency

AB=DE because corresponding parts of congruent triangles are also congruent (CPCTC)

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