Math 100
Section 5.2
Jason Siefken
Summer 2012
Anti-derivatives just seem so negative.
.
.
.
.
.
.
§5.2 Anti-derivatives
Which of the following functions is not an anti-derivative of
f(x) = 3x2 + 2?
(A) x3 + 2x
(B) x3 + 2x + 1
√
(C) x3 + 2x + 2
(D) x3 + 2x + x
(E) They’re all anti-derivatives of f
.
.
.
.
.
.
§5.2 Anti-derivatives
An anti-derivative of g is G(x) = e2x + 7. What is g?
(A) 2e2x + 7
(B) 2e2x
(C) e2x + 7
1
(D) e2x
2
(E) None of the above
.
.
.
.
.
.
§5.2 Anti-derivatives
F is an anti-derivative of f. From the graph of F, we can tell
3
F
2
1
-1
1
2
3
4
-1
(A) f is constant
(B) f is increasing
(C) f is decreasing
(D) We cannot tell anything about f
.
.
.
.
.
.
§5.2 Anti-derivatives
F is an anti-derivative of f. From the graph of F, we can tell
3
F
2
1
-1
1
2
3
4
-1
(A) f is constant
(B) f is increasing
(C) f is decreasing
(D) We cannot tell anything about f
.
.
.
.
.
.
§5.2 Anti-derivatives
∫
sin xdx is another way of saying/writing:
(A) A function whose derivative is sin x
(B) A function whose integral is sin x
(C) The function whose derivative is sin x
(D) sin x + c
(E) None of the above
.
.
.
.
.
.
§5.2 Anti-derivatives
If G(x) = 2x2 + 3 ln x − 2 is an anti-derivative of g, what other
function is an anti-derivative of g?
3
x
√
(B) (2x + 2 ln x)2
(A) 4x +
(C) 3 ln(x + 2x2 )
(D) 2x2 + 3 ln x − 1
(E) None of the above
.
.
.
.
.
.
§5.2 Anti-derivatives
F and G are both anti-derivatives of f. What could the equation of
h(x) = F(x) − G(x) be?
(A) 2x
(B) ln x
1
(C)
x
(D) ex + c
(E) 7
.
.
.
.
.
.
§5.2 Anti-derivatives
The domain of f is (−∞, ∞) and f ′ (x) > 1 for all x. F is an
anti-derivative of f. What may be true about F?
(A) F is always positive
(B) F is always negative
(C) F takes both positive and negative values
(D) F has a vertical asymptote
(E) None of the above
.
.
.
.
.
.