Recall the inverse function theorem: if f(x) has an inverse, and if f(a) = b and a = f⁻¹(b), then
f⁻¹(f(x)) = x ⇒ (f⁻¹)'(f(x)) • f'(x) = 1 ⇒ (f⁻¹)'(f(x)) = 1/f'(x)
⇒ (f⁻¹)'(b) = 1/f'(a)
Let b = 10. Then pick the function f(x) such that f(a) = 10 and f'(a) = -8 for some number a.
Answer:
100cm
Step-by-step explanation:
Width= 10
Length= 10*4= 40
10+10+40+40= 100 cm
Answer:
$960
Step-by-step explanation:
Let the original amount be = x
Percentage increase is equal to = 12.5%
final amount = original amount + increase
final amount = x + 0.125x
final amount = 1.125x
final amount = 1080 = 1.125x
and then solve for x

so in the end x is equal to $960
Solve the equation: 1080 = 1.25x
9514 1404 393
Answer:
y = -2x +1
Step-by-step explanation:
The derivative of the function is ...
f'(x) = 3x^2 -2
so the slope at x=0 is f'(0) = -2. In slope-intercept form, the equation of the tangent line is ...
y = -2x +1
Answer:
x(θ) = 5 tan θ
Step-by-step explanation:
Given that:

we are to state the trigonometric substitution to be used to find the indefinite integral.
Suppose u is the variable and a is the constant
u = x
a = 5
So; (a² + x²)ⁿ
which is a trigonometric substitution for x = a tanθ
Then,
x(θ) = 5 tan θ