Fun Facts
This function is its own derivative.
What is the exponential function?
or
What is e to the x?
This if the equation F = kx, where F is the spring force, x is the length of the spring stretch (or compression), and k is the spring constant.
What is Hooke's Law?
This German polymath has a notation named for him.
Who is Gottfried Leibniz?
This is equal to the square of the sine of x subtracted from the number 1.
What is the square of the cosine of x?
Given the proper conditions, this theorem holds that the rate of change of the directed area under a curve is the height of the leading edge.
What is the Fundamental Theorem of Calculus (Part I)?
This is the derivative of the volume of a sphere with respect to its radius.
What is the surface area of the sphere?
This method for finding the volume of a solid of revolution might help when discs and washers fail.
What is the method of cylindrical shells?
Who is Sir Isaac Newton?
This is equal to 1 more than the square of the tangent of x.
What is the square of the secant of x?
This theorem guarantees that, for a properly continuous and differentiable function, the tangent line will be parallel to the secant line somewhere on a given interval.
What is the Mean Value Theorem (MVT)?
This is the limit as x approaches 0 of sin(x) divided by x.
What is 1?
Signs analysis might help you to confirm that you have found this optimal function value.
What is the maximum value (or minimum value)?
Known for his formula eix = cos(x) + isin(x), we use his method to find new points on a curve.
Who is Leonhard Euler?
This is equal to the indefinite integral of 1 over x with respect to x.
What is the ln of the absolute value of x?
This is the limit of the difference quotient as the denominator approaches 0?
What is the derivative?
This is the area under the graph of y = sin(x) from x = 0 to x = pi.
What is 2?
Solving this type of problem can involve using implicit differentiation to produce an equation with more than one derivative and solving for one of them.
What is a related rates problem?
Famous for his error bound, this famous Italian mathematician also attempted to solve the three body problem and introduced the prime notation for derivatives.
Who is Joseph-Louis Lagrange?
This is equal to the quantity 1 plus the cosine of 2x all divided by 2.
What is the cosine square of x?
This theorem guarantees that a function will attain a maximum value and a minimum value on an interval provide the function has this feature on the closed interval.
What is continuity?
What is the value of the integral of e to the -x2 power with respect to x from negative infinity to infinity?
What is the square root of pi?
Katherine Johnson used this method to help compute trajectories for NASA.
What is Euler's Method?
This famous Greek mathematician tirelessly used the method of exhaustion to find the area of a parabolic segment.
Who is Archimedes?
This is the formula for the linearization of a function f of x at the point (a, f(a)).
What is L(x) = f(a) + f'(a)(x - a)?
If the proper conditions hold, then this theorem guarantees that a function will have a certain value over a given interval.
What is the Intermediate Value Theorem (or IVT)?