Question

Question 1. Sketch the graph of a function, any one, with the followingcharacteristics. It should be continuous on the interval (-5, 5) except for aremovable discontinuity at x = -2, a jump discontinuity at x = 1, and an infinitediscontinuity at x = 4. Realize that there is not one right answer to thisquestion, there are infinitely many right answers. As long as your functionhas the characteristics listed it is fine.Question 2.The yield, Y, of an apple orchard (measured in bushels of apples per acre)is a function of the amount x of fertilizer in pounds used per acre. Supposethat Y = f(x) = 345 + 135x.- 15x2. (a) What is the yield if 5 pounds offertilizer is used per acre? (b) Find f' (5). Give units with your answer(involving apples and fertilizer). (c) Given your answer to part (b), should moreor less fertilizer be used? Explain.

Answer 1

Given,

The function of yield is Y = f(x) = 345 + 135x - 15x^2.

a) There is 5 pounds of fertilizer used per acre.

So, x = 5,

Substituting the value of x in yield function then,

$\begin{gathered} Y=f\mleft(5\mright)=345+135(5)-15(5)^{2.} \\ =345+675-375 \\ =645 \end{gathered}$

Hence, if 5 pounds of fertilizer is used per acre then it yeild 645 bushels of apple per acre.

b)The function of yiled is Y = f(x) = 345 + 135x - 15x^2

Differentiating the function with respect to x then,

$\begin{gathered} Y=f\mleft(x\mright)=345+135x-15x^{2.} \\ f^{\prime}(x)=0+135-30x \\ f^{\prime}(x)=135-30x \end{gathered}$

The value f'(5) is,

$\begin{gathered} f^{\prime}(5)=135-30\times5 \\ f^{\prime}(5)=-15 \end{gathered}$

The value of f'(5) is -15 bushels of apple per acre.

c)Here f(5) is more than the f'(5) . The increase the yeild less fertilizer must be used.

Hence, the fertilizer are used in part b are more.