Problem

Let $ \displaystyle F(x) = \int^x_1 f(t) \, dt $,…

00:46

Problem 65 Hard Difficulty

On what interval is the curve $$ y = \displaystyle \int^x_0 \frac{t^2}{t^2 + t + 2} \, dt $$ concave downward?

Answer

$$
(-4,0)
$$

More Answers

03:55

Frank L.

Topics

Integrals

Integration

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 5

Integrals

Section 3

The Fundamental Theorem of Calculus

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Video Transcript

we know that why is crank it down on the specific intervals where why prime are the derivative is decreasing, So let's calculate the derivative first. Now we need to figure out where y double prime. In other words, the second derivative is less than zero to figure out where wide prime the first derivative is decreasing number off one G myself, you won over G squared. You can use the quotient rule because we have a numerator and denominator over here to figure this out. Zero equal to X squared plus four ax. We get access. Negative floor comma zero X squared plus works is upward opening problem. The word sister problem that opens upward there for the integral neck. The interval negative four comma zero is negative. So, in other words, negative for commas. Here is where it's con caved ounce. That's our solution

Amrita B.

Topics

Integrals

Integration

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 5

Integrals

Section 3

The Fundamental Theorem of Calculus

Top Calculus 1 / AB Educators

Heather Z.

Oregon State University

Kayleah T.

Harvey Mudd College

Caleb E.

Baylor University

Michael J.

Idaho State University