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.
Flexible Schedule
Badge
Program Modules
📍
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
DailySolve the equation y = 9 * x^(-1/2) - 4 * x^(-3/2) for the x-intercept.
quiz
✏️
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
DailyCalculate the derivative and find the tangent line equation.
quiz
📈
Finding the X-coordinate of the Maximum Point
Determine the x-coordinate of the maximum point on the curve.
Solve for Maxima
DailyFind the x-coordinate of the maximum point by setting the derivative to zero.
quiz
📐
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
DailyIntegrate and evaluate the function between x = 4 and x = 9.
quiz
What You'll Accomplish
- Find the x-intercept of a curve.
- Calculate the equation of a tangent line at a given point.
- Determine the x-coordinate of the maximum point of a curve.
- Calculate the area bounded by a curve and the x-axis.
Free for you
Full program access + updates