Differentiation - a starting investigation

Author:
Mr Creamer
Differentiation Investigation 1. Drag the slider a to see what happens to the tangent to the curve at the point (a,f(a)) 2. Select show gradient value to see a blue point which shows (a, f'(a)) - the x value is a, the y value is the gradient (or slope) of the tangent 3. "set trace" and now the blue points remain as you move the slider a. 4. Can you see a pattern in the trace points? This line or curve shows the gradient of the tangent to the curve y=f(x) for all values of x and is called f'(x) (f prime of x) 5. what is f'(x)? have a guess - say y=4x. Type your guess into the input box and see if you were right. When you have got the fright function for f'(x), note it down and move on to the next f(x) function (see below) 6. Try another function for f(x) by typing, say x^3 in the box. Note the gradient of a line with equation y=mx+c is the m value
This is an investigation, so look for patterns and try to predict what the next answer will be. 1. Find f'(x) when a) f(x) = b) f(x) = c) f(x) = d) guess for f(x) = 2. Find f'(x) when a) f(x) = b) f(x) = c) f(x) = d) guess for f(x) = 3. Advanced Find f'(x) when a) f(x) = sin(x) b) f(x) = cos(x) c) f(x) = d) guess for f(x) = ln(x)]