if we have a graph of function f(x), how can we graph the derivative of that graph without knowing the equation of that graph ?? just to sketch an approximate graph.
I know that if we have a peak then the derivative would be 0.
If the graph is increasing, would the derivative be increasing or decreasing ? would it be positive or negative ?
If we have a quadratic function then the derivative would be a line that intersect the x-axis where the peak is, don't we need another point to know how to sketch the graph ?? like the y intersect for example.
Plz help me and remember that I have to sketch it without knowing the equation, and it would be approximate.
2007-09-11 13:16:28 · 6 answers · asked by thatisme 2 in Science & Mathematics ➔ Mathematics
You are right with what you've said so far:
Where the graph hits a local maximum of minimum, then the derivative is zero (in other words, it's on the x-axis at that point)
When the graph is increasing, then the slope of the tangent lines to those points is positve, so your graph of the derivative is above the x axis. How quickly does it rise? Depends on how quickly the original increases.
Same is true for decreases, but it is below the x-axis.
Hope this helps.
Doug
2007-09-11 13:23:50 · answer #1 · answered by douglas 2 · 2⤊ 0⤋
If the graph is increasing, the derivative will be positive. The derivative may be increasing or decreasing, depending on the curvature of the graph (concave down = decreasing derivative, concave up=increasing derivative).
If you have a quadratic curve, then the derivative will be zero at the point where the curve reaches its maximum (or minimum), and is a straight line. The slope of the derivative is proportional to the amount of curvature of the function -- a tall thin parabola has a steep derivative, while a short wide parabola has a shallow derivative. Your best bet may be to find some interval over which you can estimate the slope of the quadratic accurately and use that to plot a second point to draw your line through.
2007-09-11 13:27:06 · answer #2 · answered by Pascal 7 · 1⤊ 0⤋
Derivative = slope.
When a graph is increasing, the derivative is positive. Conversely, when it is decreasing, the derivative is negative.
It is zero at a peak or a valley (point of inflection).
Think of drawing a tangent line to your graph. How does the slope of that tangent line change as you move along the graph? This will be your derivative.
Derivatives = slopes
Integrals = areas under curves
All the rest is manipulating symbols. Those are the key concepts.
2007-09-11 13:29:10 · answer #3 · answered by PMP 5 · 1⤊ 0⤋
The derivative is the RATE of CHANGE . . . if the original graph is increasing, the derivative is positive, but possibly constant, as of a linear equation. A decreasing function will have a negative derivative, but likewise it may be a constant.
As for quadratic functions, they are parabolas and have just one peak and the derivative there would be zero.
2007-09-11 13:25:52 · answer #4 · answered by Runa 7 · 1⤊ 0⤋
The derivative of a function at a certain point is the slope of the tangent line at that point.
2007-09-11 13:24:09 · answer #5 · answered by np_rt 4 · 1⤊ 0⤋
go away 6 out first. thinking x^4/a million-x write x^4= x^3*x, so as that we can write the expression as x^3(x+a million-a million)/a million-x. separate it out like x^3(x-a million)/a million-x+x^3/a million-x, this leads to (-x^3)+(x^3/a million-x) because of the fact the optimum skill of this expression is 3 and you need to locate the fourth by-product so all would be 0.
2016-11-14 23:54:47 · answer #6 · answered by bojan 4 · 0⤊ 0⤋