Daily Exam 9 – Differential Calculus

Find the equation of tangent line to the graph y = 2x³ + 4x² – 5x – 3 at point (-1, 4).

Find the equation of normal line to the graph y = x² + 1 at point (1,2).

Find the abscissa of points of inflection of y = 2x⁶ – 6x⁴.

Find the acceleration when t = 3 if s = t³ – 3t – 5.

Find the equation of the line normal to y = 2 + x – x³/3 at point (3, -4).

Find the equation of the line normal to the curve y = 3x⁵ + 10x³ + 15x + 1 at its point of inflection.

A closed box, whose length is twice its width, is to have a surface of 192 in². Find the dimensions of the box when the volume is maximum.

Differentiate y = log (x² + 1)²

Differentiate y = sec (x² + 2)

Find the slope of the line tangent to the curve y = x³ – 2x + 1 at x = 1.

Determine the equation of the line tangent to the graph y = 2x² + 1, at the point (1, 3).

The distance a body travels is a function of time and is given by x(t) = 18t + 9t². Find its velocity at t = 2.

An object is thrown vertically upward with an equation of s = 1000 + 750t – 75t². Determine the time required to reached the object on the maximum height.

The cost of C of a product is a function of the quantity x of the product: C(x) = x² – 4000x + 50. Find the quantity for which the cost is minimum. D. 1500

A function is given below. What x value maximizes y? y² + y + x² – 2x = 5.

What positive number added to its reciprocal will give the minimum sum?

The product of two positive numbers is 16. Find the number if the sum of one and the square of the other is least.

Victory liner agrees to transport 100 people or less from station A to station B for P15.00 each passenger. It was further agreed that if there are more than 100 passengers, Victory liner will reduce the fare for every passenger by P0.10 in excess of 100 passengers. What number of passengers will produce the maximum revenue for the bus company?

Water is pouring into a swimming pool. After t hours, there are t + √t gallons in the pool. At what rate is the water pouring into the pool when t = 9 hours?

Sand is pouring from a spout at the rate of 25 cc/sec. It forms a cone whose height is always 1/3 of the base radius. At what rate is the height increasing when the cone is 50 cm high?

The volume of the cube is increasing at the rate of 6 cm³/min. How fast is the surface area increasing when the length of the edge of the cube is 12 cm?

The height and base radius of a right circular cylinder are 20 cm and 8 cm respectively. If the height decreases at the rate of 3 cm/s and its base radius increases at the rate of 2 cm/s, at what rate is the volume changing?

A spherical balloon is being inflated at the rate of 40 cubic feet per minute. At the instant when the radius is 20 ft, at what rate is the surface area increasing?

If y = 4cosx + sin 2x, what is the slope of the curve when x = 2?

Find the partial derivative of 4x² — 3xy with respect to x.