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The maxima of f(x) occur at its critical points, where f '(x) is zero or undefined. We're given f '(x) is continuous, so we only care about the first case. Looking at the plot, we see that f '(x) = 0 when x = -4, x = 0, and x = 5.
Notice that f '(x) ≥ 0 for all x in the interval [0, 5]. This means f(x) is strictly increasing, and so the absolute maximum of f(x) over [0, 5] occurs at x = 5.
By the fundamental theorem of calculus,
The definite integral corresponds to the area of a trapezoid with height 2 and "bases" of length 5 and 2, so
Answer:
Step-by-step explanation:
because it's a straight angle(180)
Hello!
This expression can be broken down into 3 separate parts:
1. "the quotient of a number and (-7)"
2. "decreased by 2"
3. "is 10"
We'll begin with the first part. The word "quotient" implies the result of a division problem. Therefore, this part can be represented by the following expression (let "x" represent the unknown number):
Now we'll move on to the second part. If something is decreased by a value of 2, we know that 2 is being subtracted. Therefore, this part can be represented by the following expression:
– 2
Now we'll move on to the third and final part. The phrase "is 10" implies that the operations preceding this part are equal to 10. Therefore, this part can be represented by the following expression:
= 10
Finally, put the three parts together to create the following equation:
– 2 = 10
The equation has now been fully translated. If, however, you are required to find the unknown value (x), begin by adding 2 to both sides of the equation:
= 12
Now multiply both sides by (-7):
x = (-84)
We have now proven that the unknown number is equal to (-84).
I hope this helps!
This expression can be broken down into 3 separate parts:
1. "the quotient of a number and (-7)"
2. "decreased by 2"
3. "is 10"
We'll begin with the first part. The word "quotient" implies the result of a division problem. Therefore, this part can be represented by the following expression (let "x" represent the unknown number):
Now we'll move on to the second part. If something is decreased by a value of 2, we know that 2 is being subtracted. Therefore, this part can be represented by the following expression:
– 2
Now we'll move on to the third and final part. The phrase "is 10" implies that the operations preceding this part are equal to 10. Therefore, this part can be represented by the following expression:
= 10
Finally, put the three parts together to create the following equation:
The equation has now been fully translated. If, however, you are required to find the unknown value (x), begin by adding 2 to both sides of the equation:
Now multiply both sides by (-7):
x = (-84)
We have now proven that the unknown number is equal to (-84).
I hope this helps!