If f(3) = 7, f′(3) = −2, g(3) = 6 and g′(3) = −10, find \((g/f)'(3)\).
A−82/49
B−49/82
C−49/58
D−58/49
Mathematics · Question Bank
Differential Calculus
112 questions · page 6 of 6. Answer in your head first, then check the solution.
Find the derivative of the function \(y = \dfrac{3}{x^2 + 1}\).
A\(\dfrac{6x}{(x^2 + 1)^2}\)
B\(6x(x^2 + 1)^2\)
C\(\dfrac{-6x}{(x^2 + 1)^2}\)
D\(-6x(x^2 + 1)^2\)
Water is running out of a conical funnel at the rate of 1 cu. in/sec. If the radius of the base of the funnel is 4 in and the altitude is 8 in, find the rate at which the water level is dropping when it is 2 in from the top.
A−1/9π in/sec
B−1/2π in/sec
C1/2π in/sec
D1/9π in/sec
For what value of k will \(x + \dfrac{k}{x}\) have a relative maximum at x = −2?
A−4
B−2
C2
D4
If y = tanh x, find dy/dx.
Asech² x
Bcsch² x
Csinh² x
Dtanh² x
What number exceeds its square by the maximum amount?
A1
B1/2
C1/3
D1/4
Find the derivative of \(x^{-8}\).
A\(-8x^{-9}\)
B\(-8x^{-7}\)
C\(x^{-9}\)
D0
Find the derivative of the function \(y = \dfrac{3}{x^2 + 1}\).
A\(\dfrac{6x}{(x^2 + 1)^2}\)
B\(6x(x^2 + 1)^2\)
C\(\dfrac{-6x}{(x^2 + 1)^2}\)
D\(-6x(x^2 + 1)^2\)
Find the slope of the curve \(y = x + 2x^{-1}\) at (2, 3).
A2
B1/2
C1
D1/4
Find the maximum area of a rectangle which can be inscribed in an ellipse having the equation \(x^2 + 4y^2 = 4\).
A4
B3
C2
D5
Find the height of a right circular cylinder of maximum volume which can be inscribed in a sphere of radius 10 cm.
A11.55 cm
B14.55 cm
C12.55 cm
D18.55 cm
What is the allowable error in measuring the edge of a cube that is intended to hold 8 cu. m, if the error of the computed volume is not to exceed 0.03 cu. m?
A0.002
B0.003
C0.0025
D0.001