How do you sketch the curve #y=x^33x^29x+5# by finding local maximum, minimum, inflection points, asymptotes, and intercepts?
graph{x^33x^29x+5 [145.9, 172.6, 85.6, 73.6]} FIrst determine the interval of definition, then the behavior of first and second derivatives and the behavior of the function as
 The highest monomial is of odd order so:
 Calculate the first and second derivative:
In both points the second derivative is non null, so these are local extrema and not inflection points.
 Analyze the value of the function in the local extrema:
By signing up, you agree to our Terms of Service and Privacy Policy
To sketch the curve ( y = x^3  3x^2  9x + 5 ) and identify its local maximum, minimum, inflection points, asymptotes, and intercepts, follow these steps:

Intercepts:
 yintercept: Set ( x = 0 ) and solve for ( y ). ( (0, 5) ).
 xintercepts: Set ( y = 0 ) and solve for ( x ).

Critical Points:
 Find the first derivative ( y' ).
 Set ( y' = 0 ) and solve for ( x ).
 These are potential critical points.

Second Derivative Test:
 Find the second derivative ( y'' ).
 Substitute critical points into ( y'' ) to determine concavity.
 Use the Second Derivative Test to classify critical points as local maximum, minimum, or points of inflection.

Asymptotes:
 Vertical Asymptotes: Check for vertical asymptotes by finding where the denominator of rational functions is zero.
 Horizontal Asymptotes: Determine the behavior of the function as ( x ) approaches positive and negative infinity.

Sketching:
 Plot the intercepts.
 Use the behavior of the function near critical points and asymptotes to sketch the curve.
 Label points as local maximum, minimum, or points of inflection based on the Second Derivative Test.
These steps will help you sketch the curve and identify its key features accurately.
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a onesided 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 onesided 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 onesided 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 onesided 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.
 If #( x+2) / x#, what are the points of inflection, concavity and critical points?
 How do you find all critical point and determine the min, max and inflection given #f(x)=x^3+x^2x#?
 For what values of x is #f(x)= x^2x + 1/x1/x^2 # concave or convex?
 How do you find all points of inflection given #y=x^32x^2+1#?
 How do you find the second derivative of #sqrtx#?
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7