In parts (a)-(c), sketch a continuous curve y = f x with the stated properties. (a) f 2 = 4 , f ′ 2 = 0 , f ″ x > 0 for all x (b) f 2 = 4 , f ′ 2 = 0 , f ″ x < 0 for x < 2 , f ″ x > 0 for x > 2 (c) f 2 = 4 , f ″ x < 0 for x ≠ 2 and lim x → 2 + f ′ x = + ∞ , lim x → 2 − f ′ x = − ∞
In parts (a)-(c), sketch a continuous curve y = f x with the stated properties. (a) f 2 = 4 , f ′ 2 = 0 , f ″ x > 0 for all x (b) f 2 = 4 , f ′ 2 = 0 , f ″ x < 0 for x < 2 , f ″ x > 0 for x > 2 (c) f 2 = 4 , f ″ x < 0 for x ≠ 2 and lim x → 2 + f ′ x = + ∞ , lim x → 2 − f ′ x = − ∞
Find the set of values of y=2x+k meets the curve y=1+2kx-x² at 2 distinct points?
Parameterize the following portions of curves:
(a) e
The straight line between (-5, 3) and (11, 11).
(b) A portion of the function f(x) = r* + 1 from (1, 2) to (-2,-7)
Three-quarters of the unit circle traversed counter-clockwise, starting at (1,0).
8) Let f(x)=3x-2√√x
(a) Find the equation of the secant line through the points (4,f(4)) and (9, ƒ(9)).
(b) Show that there is only one number c in the interval (4,9) that satisfies the
conclusion of the Mean-Value Theorem for the secant line in part (a).
(e) Find the equation of the tangent line to the graph of fat the point (c, ƒ (c)).
(d) Use a graphing utility to graph the secant line in part (a), and the tangent line in
part (c) in the same coordinate system, and confirm that the two lines are parallel.
Precalculus: Mathematics for Calculus - 6th Edition
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