Help with functions?
1 answer:
Answer:
The function g(x) = - x² + 14x + 39 is at a minimum when x = 7 is not true i.e. false.
Step-by-step explanation:
The function is given to be g(x) = - x² + 14x + 39 .......... (1)
Now, the condition for maxima or minima is .
Now, differentiating equation (1) we get, g'(x) = - 2x + 14 ........ (2)
Hence, for maxima or minima g'(x) = 0 = - 2x + 14
⇒ x = 7
Now, from equation (2) and differentiating both sides with respect to x again < 0
Therefore,the function g(x) has maxima at x = 7
Therefore, the function g(x) = - x² + 14x + 39 is at a minimum when x = 7 is not true i.e. false.
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Answer:
lateral surface area = 48 inches²
Step-by-step explanation:
The picture below is the square base pyramid you are referring. The lateral area is adding the area of the 4 triangles in the pyramid.
area of a triangle = 1/2 × b × h
The slant height of the triangle is gotten using Pythagoras theorem
lateral surface area = 4 × (1/2 × 3 × 8)
lateral surface area = 4 × 24/2
lateral surface area = 4 × 12
lateral surface area = 48 inches²
Answer:
y - 7 = 4(x - 35)
Step-by-step explanation:
The fundamental theorem of calculus states that:
= f(x).
So using the fundamental theorem of calculus, you can find that h'(x) = f(x).
The question tells you that f(x) is periodic with a period of 8, so f(x) repeats itself every 8 units.
Using this, you can find that the slope of h(x) at x = 35 is the same as the slope of h(x) at x = 3, which is 4.
The slope of h(x) at x = 35 is 4.
Now I have to find the value of h(x) when x = 35. It is the area under f(x) from 0 to 35.
The area underneath f(x) from 0 to 35 is 7. When x = 35, h(x) = 7.
Now use the point-slope formula to write the equation of the tangent line.
The answer is <u>y - 7 = 4(x - 35)</u>