Does anyone know how to do this. that can show me the work ? ?
-view attachment

SOH CAH TOA
Sine=opposite leg/hypotenuse
Cosine=adjacent leg/hypotenuse
Tangent=opposite leg/adjacent leg
SOH CAH TOA
So d is the correct answer

Yourself by using the internet

Answer

1 number

explanation

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

 

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.