f(x)=(x+5)^4 ; x= - 5
Decide if the given value of x is a criticial number for f, and if so, decide whether the point is on f is a relative minimum, relative maximum, or neither.
The answer is : Critical number; minimum at ( - 5, 0)
NOTE: use the first derivative.
I have the answer but I don't understand how to get to it...Can you please show me steps? Thank you.
Decide if the given value of x is a criticial number for f, and if so, decide whether the point is on f is a relative minimum, relative maximum, or neither.
The answer is : Critical number; minimum at ( - 5, 0)
NOTE: use the first derivative.
I have the answer but I don't understand how to get to it...Can you please show me steps? Thank you.
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Take the derivative and set it equal to 0.
f(x) = (x+5)^4
f '(x) = 4(x+5)^3
4(x+5)^3 = 0
//Divide both sides by 4
(x+5)^3 = 0
//Take the cube root of both sides
x+5 = 0
//Subtract 5 from both sides
x = -5
So -5 is a critical number.
It is also a relative minimum since (x+5)^4 is a parabola, -5 is the bottom part of it. Hope that helps.
f(x) = (x+5)^4
f '(x) = 4(x+5)^3
4(x+5)^3 = 0
//Divide both sides by 4
(x+5)^3 = 0
//Take the cube root of both sides
x+5 = 0
//Subtract 5 from both sides
x = -5
So -5 is a critical number.
It is also a relative minimum since (x+5)^4 is a parabola, -5 is the bottom part of it. Hope that helps.
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no