Q: (a) If f (x) = (x3 –
(a) If f (x) = (x3 – x)ex, find f ‘(x). (b) Check to see that your answer to part (a) is reasonable by comparing the graphs of f and f ‘.
See AnswerQ: The equation y’’ + y’ – 2y = x2 is called a
The equation y’’ + y’ – 2y = x2 is called a differential equation because it involves an unknown function y and its derivatives y’ and y”. Find constants A, B, and C such that the function satisfies y...
See AnswerQ: Find a cubic function y = ax3 + bx2 + cx +
Find a cubic function y = ax3 + bx2 + cx + d whose graph has horizontal tangents at the points (-2, 6) and (2, 0).
See AnswerQ: Find a parabola with y = ax2 + bx + c equation
Find a parabola with y = ax2 + bx + c equation that has slope 4 at x = 1, slope -8 at x = -1, and passes through the point (2, 15).
See AnswerQ: Let / Is f differentiable at 1?
Let Is f differentiable at 1? Sketch the graphs of f and f ’.
See AnswerQ: At what numbers is the following function g differentiable?
At what numbers is the following function g differentiable? Give a formula for g’ and sketch the graphs of g and g’.
See AnswerQ: Find the parabola with y = ax2 + bx equation whose tangent
Find the parabola with y = ax2 + bx equation whose tangent line at (1, 1) has equation y = 3x - 2.
See AnswerQ: Suppose the y = x4 + ax3 + bx2 + cx +
Suppose the y = x4 + ax3 + bx2 + cx + d curve has a tangent line when x = 0 with equation y = 2x + 1 and a tangent line when x − 1 with equation y = 2 - 3x. Find the values of a, b, c, and d.
See AnswerQ: For what values of a and b is the line 2x +
For what values of a and b is the line 2x + y = b tangent to the parabola y = ax2 when x = 2?
See AnswerQ: Differentiate the function. f(t) = 1.
Differentiate the function. f(t) = 1.4t5 – 2.5t2 + 6.7
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