The bottom of a river makes a V-shape that can be modeled with the absolute-value function d(h) =
1
3
|h − 153| − 51,
where d is the depth of the river bottom (in feet) and h is the horizontal distance to the left-hand shore (in feet).
A ship risks running aground if the bottom of its keel (its lowest point under the water) reaches down to the river bottom. Suppose you are the harbormaster and you want to place buoys where the river bottom is 30 feet below the surface. How far from the left-hand shore should you place the buoys?
Complete the absolute-value equation. Solve the equation and determine which, if any, of the solutions are appropriate.

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explanation:

1 number

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.

i need a picture

step-by-step explanation: