and t (b) 38 (d) r42 and (b 42 (o) 40 and -42 44 What are your conclusions? 8. T 3. The point P(2, -1) lies on the curve y (a) If Q is the point (x. 1/(1 the slope of the secant line PQ (correct to six decimal places) for the following values of x: (0 1.5 1/(1 x). x)), use your calculator to find i) 1.9 (vi) 2.1 i) 1.99 (iv) 1.999 (vii) 2.01 (viii) 2.001 () 2.5 (b) Using the results of part (a), guess the value of the slope of the tangent line to the curve at P(2, -1). (c) Using the slope from part (b), find an equation of the tangent line to the curve at P(2. -1). noint Pi0 5 01 lio
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.
I am doing homework for Calculus and I am having trouble with #3 tangent problem on Secction 2.1 of the James Stewart Calculus Eighth Edition, page 82. I need some hints on what to do on the first (a) part of the question, please?
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