If there are no critical values, enter None. If there are more than one, enter them separated by commas. B Use interval notation to indicate where f x is increasing and also decreasing.
C Find the x-coordinates of all local maxima and local minima of f. D Use. Find the intervals on which f x is concave up and the intervals where it is concave down. Show a sign graph. Please show work in detail so I can follow for future reference. Is there no solution because the equation can't be factored?
At what. Okay, I need major help! Can someone tell me if these statements are true or false ASAP please. Thank you. Find the interval. Simplify terms. Cancel the common factor of. Move the leading negative in into the numerator. Cancel the common factor. Rewrite the expression. Simplify and combine like terms. Multiply by by adding the exponents. Solve the equation. Subtract from both sides of the equation. Divide each term by and simplify. Divide each term in by. Divide by. Take the root of both sides of the to eliminate the exponent on the left side.
The complete solution is the result of both the positive and negative portions of the solution. Simplify the right side of the equation.
Rewrite as. Pull terms out from under the radical, assuming positive real numbers. First, use the positive value of the to find the first solution.
Next, use the negative value of the to find the second solution. Find the points where the second derivative is. Substitute in to find the value of. Replace the variable with in the expression. Simplify the result. Expand by moving outside the logarithm. The final answer is. The point found by substituting in is. This point can be an inflection point. Determine the points that could be inflection points. Substitute a value from the interval into the second derivative to determine if it is increasing or decreasing.
Simplify the denominator. At , the second derivative is. Since this is negative, the second derivative is decreasing on the interval. Decreasing on since. Raising to any positive power yields.
Reduce the expression by cancelling the common factors. Cancel the common factor of and. Cancel the common factors. Since this is positive, the second derivative is increasing on the interval. Increasing on since. An inflection point is a point on a curve at which the concavity changes sign from plus to minus or from minus to plus.
The inflection points in this case are. Find the domain of. Set the argument in greater than to find where the expression is defined.
Subtract from both sides of the inequality. Since the left side has an even power , it is always positive for all real numbers. The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined. Interval Notation:.
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