Calculus Problem: Curve Analysis and Tangents

A step-by-step walkthrough of a calculus problem involving curve equations, finding x-intercepts, tangent lines, maximum points, and area calculation.

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Program Modules

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Finding the X-coordinate of Point A

Determine the x-coordinate of the point A where the curve crosses the x-axis.

Solve for x-intercept

Daily

Solve the equation y = 9 * x^(-1/2) - 4 * x^(-3/2) for the x-intercept.

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Finding the Equation of the Tangent at A

Determine the equation of the tangent line to the curve at point A (4, 0).

Tangent Line Calculation

Daily

Calculate the derivative and find the tangent line equation.

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Finding the X-coordinate of the Maximum Point

Determine the x-coordinate of the maximum point on the curve.

Solve for Maxima

Daily

Find the x-coordinate of the maximum point by setting the derivative to zero.

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Finding the Area Bounded by the Curve

Calculate the area bounded by the curve, the x-axis, and the lines x = 4 and x = 9.

Calculate Definite Integral

Daily

Integrate and evaluate the function between x = 4 and x = 9.

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