Questions from General Calculus

Q: Find equations of the tangent line and normal line to the curve

Find equations of the tangent line and normal line to the curve at the given point. y2 = x3, (1,1)

Q: Differentiate the function. f(x) = e5

Differentiate the function. f(x) = e5

Q: Find an equation of the tangent line to the curve at the

Find an equation of the tangent line to the curve at the given point. Illustrate by graphing the curve and the tangent line on the same screen. y = 3x2 – x3, (1, 2)

Q: Find dy/dx by implicit differentiation. tan-1

Find dy/dx by implicit differentiation. tan-1(x2y) = x + xy2

Q: Find equations of the tangent line and normal line to the given

Find equations of the tangent line and normal line to the given curve at the specified point. y = 2x / x2 + 1 , (1, 1)

Q: Find an equation of the tangent line to the curve at the

Find an equation of the tangent line to the curve at the given point. Illustrate by graphing the curve and the tangent line on the same screen.

Q: Find f’(x). Compare the graphs of f and f’

Find f’(x). Compare the graphs of f and f’ and use them to explain why your answer is reasonable. f(x) = x4 – 2x3 + x2

Q: Find f’(x). Compare the graphs of f and f’

Find f’(x). Compare the graphs of f and f’ and use them to explain why your answer is reasonable.

Q: (a) Graph the function f(x) =

(a) Graph the function f(x) = x4 – 3x3 – 6x2 + 7x + 30 in the viewing rectangle [-3,5] by [-10,50]. (b) Using the graph in part (a) to estimate slopes, make a rough sketch, by hand, of the graph of f...

Q: (a) Graph the function g(x) − ex

(a) Graph the function g(x) − ex - 3x2 in the viewing rectangle [-1, 4] by [-8, 8]. (b) Using the graph in part (a) to estimate slopes, make a rough sketch, by hand, of the graph of t9. (See Example 2...