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Unformatted text preview: Practice Test 2B for Math 1501 (I) Let f be the function deﬁned by f (x) = 1+ √ x for x = 0 (a) Find the equation for the tangent line to the graph of y = f (x) at the point (9, 2). (b) Find the intersection of this tangent line with the x axis. (II) Consider the curve given by x4 + y 4 = 1 . (Note the fourth powers; this is not the unit circle.) (a) Find the points where the line y = 21/4 x crosses this curve. (b) Find the equation for the tangent line to the curve at each of the points found in part (a). (III) Let f ( x) = A x3 + 1 , x ≥ 1 Bx + 2, x < 1 . (a) For what values of A and B is f diﬀerentiable for all x? (b) With these values of A and B , what is the equation of the tangent line to f at x = 1? (IV) A ladder 5 meters long is leaning against a wall. If the foot of the ladder is pulled away from the wall at a rate of 1 meter per second, how fast will the top of the ladder be falling at the instant when the base is 3 meters from the wall? (V) (a) Given a function f with f (2) = 2 and f (2) = 3. Compute d f (f (x)) dx at x = 2. (b) Compute the derivative of (c) Compute the derivative of (cos(x)) (d) Compute the derivative of arcsin(ln(x)) .
sin(x) x2 tan(x2 ) , , for − π/2 < x < π/2 ...
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