Derivatives
The first derivative of
x10 - 3x + 1.
What is...
10x9 - 3
The anti-derivative of 10x4 - 3x2 + 1
What is...
2x5 - x3 + x + C
The acceleration of an object given that its velocity is v(t) = 3t + 1.
What is...
3.
The solution of the simultaneous solutions:
1) 4.77x - 3y = 10
2) 10x + 2.8y = 100
(Rounded to 2 d.p.)
What is...
(7.57, 8.70)
The gradient of
f(x)=3x3 - x2 + 4x - 1
at the point (1, 5).
What is...
11
Integrate f(x) = 12x twice.
What is...
2x3 + Cx + D
The acceleration of an object with a displacement function of s(t) = 4t2 - t + 2
What is...
8
The solution(s) of 2x2 + 3x - 1 = 0. (Rounded to 2 d.p.)
What is...
x1 = 0.28..., x2 = -1.78...
The coordinate of the minimum point of the function f(x) = 3x2 + 12x - 1.
What is...
(-2, -13)
The function f(x) given f'(x) = 12x - 3 and the coordinate (-1, 11) lies on the curve of f(x).
What is...
f(x) = 6x2 - 3x + 2
The velocity function of an object that has an acceleration of -3m/s2 and an initial velocity of 50m/s.
v(t) = -3t + 50
The intersection point between f(x) = x2 - 2 and g(x) = 4x3 + 7. (Rounded to 2.d.p.)
What is...
(-1.23, -0.48)
The coordinate of f(x)=2x2 - 4x where the gradient is -2.
What is...
(0.5, -1.5) or (1/2, -3/2)
The function f(x) given that
f'(x) = -8x3 + 7x and f(x) has an x-intercept at x=2.
What is...
f(x) = -4x4 + 3.5x2 + 50
What is...
s(t) = t2 + 5t
The coordinates of the maximum point of f(x) = 4x3 + x2 - 5x. (Rounded to 2 d.p.)
What is...
(-0.73, 2.63)
The maximum area of a rectangle, if its perimeter needs to be 30cm.
What is...
56.25 cm2
The function f(x) given that it has a minimum point at (1, 2) and f'(x)= x + k.
What is...
f(x) = 0.5x2 - x + 2.5
The time that an object with a displacement function of s(t) = 4t - t2 is at rest.
What is...
t = 2
The x-values of the stationary points of the function f(x)=x4 - 5x3 + 6x2 + 4x - 8.
What is...
x1 = -0.25 and x2 = 2