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What is its maximum height? Using derivatives we can find the slope of that function: h' = 0 + 14 − 5 (2t) = 14 − 10t. (See below this example for how we found that derivative.) Now find when the slope is zero: 14 − 10t = 0. 10t = 14. t = 14 / 10 = 1.4. The slope is zero at t = 1.4 seconds. And the height at that time is: h = 3 + 14×1.4 − 5×1.4 2.
- Second Derivative
Example: A bike race! You are cruising along in a bike race,...
- Differentiable
Because when a function is differentiable we can use all the...
- Continuous
Example: How about this piecewise function: It looks like...
- Second Derivative
2 Δεκ 2015 · A ball is thrown into the air with an initial velocity of $16 ft/s$. its height after $t$ seconds is given by $f(x) = 16t-4t^2$ . After how many seconds does the ball reach its maximum height? I c...
Finding the maximum and minimum values of a function also has practical significance because we can use this method to solve optimization problems, such as maximizing profit, minimizing the amount of material used in manufacturing an aluminum can, or finding the maximum height a rocket can reach.
Finding the maximum and minimum values of a function also has practical significance because we can use this method to solve optimization problems, such as maximizing profit, minimizing the amount of material used in manufacturing an aluminum can, or finding the maximum height a rocket can reach.
10 Νοε 2020 · Finding the maximum and minimum values of a function also has practical significance, because we can use this method to solve optimization problems, such as maximizing profit, minimizing the amount of material used in manufacturing an aluminum can, or finding the maximum height a rocket can reach.
25 Ιουλ 2024 · The maxima of a function are defined as the point in the given interval where the function value is maximum. In other words, maxima is the highest point on the curve of a function. There are two types of maxima: Local or Relative Maxima. Absolute or Global Maxima. Minima Definition.
The height of the function at "a" is greater than (or equal to) the height anywhere else in that interval. Or, more briefly: f (a) ≥ f (x) for all x in the interval. In other words, there is no height greater than f (a). Note: "a" should be inside the interval, not at one end or the other.
