Derivatives
What is the derivative of 8x^9
72x^8
What rule is used when 0/0 is obtained when solving for the limit of a function
L\'Hôpital's rule
Antiderivative of x^9
x^10/10
Cross-section formula of a triangle
A = (1/2) * base * height
What theorems need to only be continuous
(IVT, EVT)
What is the derivative of 12x^5+5x^3+2x^2
60x^4+15x^2+4x
lim as h approaches 0 of f(x+h)-f(x)/h what is this called
Definition of derivative
Antiderivative of 3x^4+5x^7
3x^5/5+5x^8/8
Cross-section formula of a semicircle
Area = (1/2) * π * r²
What theorems need to be both continuous and differential
(MVT and Rolle's)
What is the derivative of 9x^2·4x
108x^2
lim as x approaches 4 of x^3+2x^2+7x/x-4
71/-4
Antiderivative of (3x^2)(8x+3)
6x^4+3x^3
Cross-section formula of a trapezoid
A = (1/2) * (a + b) * h
Given that f(x) is differentiable f(x)=3x^3+9x^2+5x+4, is there a value c on 0<c<9 such that f(c) = 30 What theorem would be used to solve this
(IVT)
What is the derivative of 5x^3(2x)
40x^3
lim as x approaches 5 of (x-9)(2x^3+4x^2+6x)/ x-5
404/5
Integral from 2 to 4 of 3x^4
2976/5
Cross-section formula of an equilateral triangle
A = (√3/4) * s²
Given that g(x) is differentiable g(x)=2x^3+4x^2+7x+2, is there a value c on 0<c<9 such that g(c) = 42 (Solve)
g(0)=2
g(9)= 1847
Since g(x) is cont as it is dif and 42 is between g(0) and g(9) , by IVT there exists some c value between 0 and 9 such that g(c) = 42
What is the derivative of 2x^3+5x^2/7x^3+3x^2
-29/(7x+3)^2
lim as x approaches 9 (x^2+5x)(2x^2+4x)(6x+4)/x-9
706740/9
Integral from 1 to 5 of 5x^2+6x+2
860/3
Cross-section formula of a parallelogram
Area = base * height
Let f(x) be a differentiable function with these selected values x(1,2,4,8,14) f(x)(-9,-7,4,9,5)
Is there a c value, 1<c<11 such that f prime of c is equal to 1
14-2/5+7 = 1
Since f(x) is dif MVT applies
Therfore there is a value c from 1<c<14 that exist by MVT