Derivatives
Integrals
Antiderivatives
Relative Min/Max Points
200
WHAT IS THE DERIVATIVE OF THE FUNCTION f(x)= 5?
f‘(x) = 0
200
PROVIDE THE INTEGRAL OF THE FUNCTION f(x) = 12x OVER THE INTERVAL 1 ≤ x ≤ 6
int_1^6 (12x)dx
200
WHAT IS THE ANTIDERIVATIVE OF f(x)=
3x^2 + x ?
200
WHAT IS THE RELATIVE MINIMUM OF
f(x) = x^2
(0,0)
400
WHAT IS THE DERIVATIVE OF
f(x)=
3x^2 -2x + 1?
f‘(x) = 6x - 2
400
PROVIDE THE INTEGRAL OF THE FUNCTION f(x)=
3x^6 + 19x^2 + 4
FROM THE DOMAIN
2 < x ≤ 13
400
WHAT IS THE ANTIDERIVATIVE OF
f(x)= 9x^3 + 5x^2
F(x) = 
400
WHAT IS THE RELATIVE MAXIMUM OF
f(x) = 3x^2+ 2x^2 - 4x + 2
(-.925, 5.04)
600
WHAT IS THE DERIVATIVE OF f(x)=
4x + 5x^5 + 4x^-2 - 2
f'(x) =
25x^4 - 8/x^3 + 4
600
WRITE THE INDEFINITE INTEGRAL OF THE FUNCTION f(x)=
4x^2 + 9x - 27
int 4x^3/3 + 9x^2/2 - 27x + c, c in RR
600
WHAT IS THE ANTIDERIVATIVE OF f(x)=
-4x^3 + 13x^2 -7x + 42
F(x) =
-x^4 + 13x^3/3 -7x^2/2 + 42x + C;C in RR
600
If f(x) =
-2x^2
, WILL YOU FIND A RELATIVE MINIMUM OR MAXIMUM POINT?
MAXIMUM
800
WHAT IS THE DERIVATIVE OF
sqrtx
f‘(x) =
1/2sqrtx
800
SOLVE THE DEFINITE INTEGRAL WITH YOUR GDC
int_2^6(8x^4 - 4x^3 + 37x)dx
11,702.4 or
11,700
800
WHAT IS THE ANTIDERIVATIVE OF f(x)=
-8x^5 + 21x^3 - 58x + 32
F(x) =
800
WHAT IS THE RELATIVE MINIMUM OF
f(x) = .02x^2+12x- 18?
(-30, -198)
1000
WHAT IS THE DERIVATIVE OF f(x) =
-x^-2 + 5x +3x^2 - 19x^3
2/x^3 + 5 +6x - 57x^2
1000
(hint: rate of change)
FORD’S PROFIT, P, IN MILLIONS, CHANGES DEPENDING ON HOW MANY CARS ARE PRODUCED, IN THOUSANDS. REPRESENTED BY
dP/dx=-2.5x+32, x≥0,
THIS MONTH, FORD MAKES A PROFIT OF $43 MILLION BY SELLING 7,500 CARS. SOLVE FOR c (3 S.F.) AND REWRITE THE EXPRESSION P IN TERMS OF x
C ≈-188
P(x)= 1.25x^2 + 32x - 188
1000
WHAT IS THE ANTIDERIVATIVE OF
f(x)=432x^18-23x^4+2x^7-42x^2+892?
F(x)=(432x^19)/19+x^8/4-(23x^5)/5-14x^3+892x + C;C in RR
1000
WHAT IS THE RELATIVE MINIMUM OF f (x) =
6x^2+1 ?
(0,1)