How do you sketch the graph #y=x^3+2x^2+x# using the first and second derivatives?
Refer Explanation section
Given -
graph{x^3+2x^2+x [-10, 10, -5, 5]}
.
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To sketch the graph of ( y = x^3 + 2x^2 + x ) using the first and second derivatives:
- Find the first derivative: ( \frac{dy}{dx} = 3x^2 + 4x + 1 ).
- Set ( \frac{dy}{dx} ) equal to zero and solve for ( x ) to find critical points.
- Use the second derivative test to classify the critical points as local maxima, local minima, or points of inflection.
- Sketch the graph based on the behavior of the first and second derivatives.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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- What is the second derivative of #f(x)= sin(sqrt(3x-7))#?
- How do you find the x coordinates of all points of inflection, final all discontinuities, and find the open intervals of concavity for #y=sinx+x# for #[-pi,5pi]#?
- Is #f(x)=-x^3-12x^2-14x-2# concave or convex at #x=0#?

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