Answer:
x = -6 and x = 4
Step-by-step explanation:
In math, the critical points of a function are the points where the derivative equals zero.
So, first we will find the derivative of the function. The derivative is:
Now, we are going to make the derivative equal zero and find the answers of the equation.
So we have that the critical points are the answers to this equation:
and
Thus, the critical points are x=-6 and x=4
Answer:
x = 3/2 or x = -5/4
Step-by-step explanation:
Solve for x over the real numbers:
8 x^2 - 2 x - 15 = 0
Using the quadratic formula, solve for x.
x = (2 ± sqrt((-2)^2 - 4×8 (-15)))/(2×8) = (2 ± sqrt(4 + 480))/16 = (2 ± sqrt(484))/16:
x = (2 + sqrt(484))/16 or x = (2 - sqrt(484))/16
Simplify radicals.
sqrt(484) = sqrt(4×121) = sqrt(2^2×11^2) = 2×11 = 22:
x = (2 + 22)/16 or x = (2 - 22)/16
Evaluate (2 + 22)/16.
(2 + 22)/16 = 24/16 = 3/2:
x = 3/2 or x = (2 - 22)/16
Evaluate (2 - 22)/16.
(2 - 22)/16 = -20/16 = -5/4:
Answer: x = 3/2 or x = -5/4
Answer:
x ≤ 1
Step-by-step explanation:
Swapping sides of the inequality requires reversing its sense.
If 1 is greater than x, then x is less than 1.
Answer:
H0 : μ = 15
H1 : μ < 15
−6.170774
Step-by-step explanation:
Given :
n=115, barx =11.3, and s=6.43
H0 : μ = 15
H1 : μ < 15
−0.053658 ;
The test statistic :
(xbar - μ) ÷ s/sqrt(n)
(11.3 - 15) ÷ (6.43/sqrt(115))
Test statistic = −6.170774
Rejection region :
Reject Null ; if
Tstatistic < Zcritical
The P value is 0.00001 ; using the p value from Z calculator
Since,
P value < α
0.00001 < 0.05
Reject the null
