Horizontal Tangent Line In Exercises 63–70,determine the point(s) (if any) at which the graphof the function has a horizontal tangent line.. 68. y = x + 4ex
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Horizontal Tangent Line In Exercises 63–70,
determine the point(s) (if any) at which the graph
of the function has a horizontal tangent line..
68. y = x + 4ex
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- Horizontal Tangent Line In Exercises 63–70,determine the point(s) (if any) at which the graphof the function has a horizontal tangent line. \text { 65. } y=\frac{1}{x^{2}}Finding a horizontal tangent line Determine whether the graph ofƒ(x) = xx, for x > 0, has any horizontal tangent linescalculus Find the equation of the tangent line to the graph of f(x) = 4 - x2 at point (1,3).
- Determining Differentiability. Describe the x-values at which f is differentiable.Explain your understanding of the connection between the derivative of a constant and the slope of the tangent of a function. Use a diagram in your solutionLooking for help starting with the 3rd bullet point: "Find the equation of the tangent line..."
- Famous Curves In Exercises 39–42, find theslope of the tangent line to the graph at the givenpoint.Straight line (What is its equation?)Mean Value Theorem and graphs By visual inspection, locateall points on the interval (-4, 4) at which the slope of the tangentline equals the average rate of change of the function on the interval [-4, 4].
- How many tangent lines to the curve y = x / (x + 5) pass through the point (1, 2)? At which points do these tangent lines touch the curve? Smaller x-value (x,y): Larger x-value (x,y):Explain how the real-world meaning of a derivative is related to the independent (input) and dependent (output) variables of the problem. Use your explanation in a real-world contextual situation of your choosing. Also, include a sketch of the two axes (independent and dependent) that you use to help clarify your discussion for the reader. Please explain and sketch a graph of two axes.A thin observatory probe having the shape of a plate is probing a volcano in an xy −plane at a point P(x, y). The probe can only withstand a certain amount of temperature; thus, Represent the temperature as the function of x and y when the temperature calculated in degrees Celsius is inversely proportional to the square of its distance from theorigin.