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PRACTICE SECOND MIDTERM
Math 2A
1. Given the function
f(x) = x4โ6x2,
find the open intervals at which the function is monotonic increasing/decreasing, and the
intervals at which the function concave up and concave down. Identify the local maxima, the
local minima, and the inflection points. Identify the asymptotes of this function, if they exist,
and classify them. Sketch of the graph of the function.
2. Given the function
f(x) = x3
x2โ4
find the open intervals at which the function is monotonic increasing/decreasing, and the
intervals at which the function concave up and concave down. Identify the local maxima, the
local minima, and the inflection points. Identify the asymptotes of this function, if they exist,
and classify them. Sketch of the graph of the function.
3. You are designing a poster to contain 50in2of printing with margins of 4in at each the top
and the bottom, and 2in at each side. What overall dimensions of the poster will minimize
the amount of paper used?
4. Find the absolute maximum and the absolute minimum of the function
f(x) = 2 โ(xโ1)2/3
in:
(a) the interval [0,9],
(b) the interval [9,โ).
5. A window has the shape of a square surmounted by a semi-circle. The base of the window is
measured as having a width of 60cm with a possible error in the measurement of 0.1cm. Use
differentials to estimate the maximum error possible in computing the area of the window.
6. Write an equation of the line tangent to the curve
y=qx+โx+ 1
at the point (0,1).
