7. Ship A is traveling due west toward Lighthouse Rock at a speed of 15 km/hr. Ship B is N traveling due north away from Lighthouse Rock at a speed of 10 km/hr. Let x be the distance between Ship A and Lighthouse Rock at time t, and let y be the distance between Ship B and lighthouse rock at time t. (a) Find the distance between Ship A and Ship B when x = 4 km and y = 3 km. Ship B -E (b) Find the rate of change of the distance between the two ships when x = 4 km and y = З кт. (c) Let 8 be the angle shown in the figure. Find the rate of change of e in radians per hours Ship A Lighthouse Rock when x = 4 km and y = 3 km.

Q: The point on the curve y = 2-x nearest to (3,2) is (1,1) (0,2)

A:

Q: [3] If the curve is defined by y = x* – 8x3 + 22x2-24x+9, then what are the value/s of x for which…

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Q: 2 Find an equation of the line L, where L is perpendicular to y =x and passes through the point…

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A:

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A: Let's Solve, Answer : Option E

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Q: The curve y=ax^2+bx+c passes through the point (1,9) and is tangent to the line y=3x at the origin.…

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Q: 11. Find k if the curve y=x +k is tangent to the line y= 2x.

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Q: 4. xy²1₁ X=1, x = 4, y = 0; about the x-axis

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Q: 4. At what point on the graph of y = ÷x² is the tangent line parallel to the line 2x – 4y = 3? A.…

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Q: Designer functions Design a sine function with the givenproperties.

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Q: 6. Find the member of the curve whose slope at any point is √y and passes through the point (2, 1)

A:

Q: 6. Find the length of the curve y =-+ from x =1 to x=2. 9. 28x

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Q: find the length of the curve on the given interval: y = 4/3 (x+1) ^ (3/2), [0,3]

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Q: 5 Find the equation of line tangent to the curve y= x+ at point P(1,3) A None of the given choices…

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Q: 1 Find the points of discontinuity of y = where и +и - 2 1 u = * - 1

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Q: 4) Find a formula for the line tangent to the curve at the point (4,4).

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Q: Let (21, Y1) = (7,9), m = 3. Then the equation of the tangent line is O y = 3x- 20 O y = 3r - 16 O y…

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Q: 4. Find the equation for the line tangent to (persamaan garis şinggung) a. y= x2- 3 x + 5 at the…

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Q: Show that the line y = -10x + 20 is tangent to the curve y = x4 – 4x^3 – 5x^2 + 26x – 16.

A:

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A:

Q: Find the condition that the line ax+by=1 may be normal to the curve an-1y

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A: We will use differentiation and slope of line to solve this.

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.