9. Let f (x) = x^3 − 10. Find all numbers c in the interval (-11,...

9. Let f (x) = x^3 − 10. Find all numbers c in the interval (-11, 11) for which the line tangent to the graph of f is parallel to the line joining (−11, f (−11)) and (11, f(11)). How many such numbers exist in the given interval?

. 0

. 1

. 2 (correct)

. 3

Enter points in increasing order (smallest first). Enter DNE in any empty answer blank.

c =

c = DNE (correct)

10. Let g(x) = x² − (5/x)

First find the slope m of the line joining (1, g(1)) and (2, g(2)). Then use the Newton-Raphson method to estimate the values of c for which g'(c) = m. Check that your calculator is set for at least 10 digit display. Continue the process until successive iterations obtained by the calculator are identical.

m = 0.5 (incorrect)

1 (correct)

3
Enter values of c below in order from least to greatest. Enter DNE in any empty answer blanks.
c =
c = DNE (correct)
c = DNE (correct)

11. A landowner wishes to use 15 miles of fencing to enclose an isosceles triangular region of as large an area as possible. What should be the lengths of the sides of the triangle?
Let x be the length of the base of the triangle. Write the area as a function of x. [First write the length of the equal-length sides in terms of the base, x, then write the height of the triangle in terms of the base.]

A(x) =_______________

Length of base = ____________ miles

Length of the other two (equal-length) sides = ______________ miles each

Solutions

Expert Solution

Find derivative of given function also the values of function at given point to find slope of tangent at c and slope of line passing through given point. Then set both slopes equal to get required answer.

milcah answered 1 year ago

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