perplexus.info :: Just Math : No calculus

No calculus (Posted on 2002-07-31)

Define:
d/dx(f(x)) = f'(x)

where f'(x) = gradient (or slope) of f(x) at x = x.

Prove that:
d/dx(x^2) = 2x

without using calculus.

See The Solution Submitted by Cheradenine

Rating: 3.2000 (10 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

Puzzle Solution

Comment 26 of 26 |

Let y= Cx+D be a tangent to y= x^2.

Then, there is precisely one solution to the quadratic equation:

x^2-Cx-D =0

Then, C^2=4CD

=> C= 4D

Therefore:

x=-(-D)/2C = D/2*1 = D/2

=> D= 2x

Now, in y= Cx+D, C is the gradient.

Therefore, d/dx(x^2)= 2x

Edited on January 29, 2024, 7:25 am

Posted by K Sengupta on 2024-01-29 07:18:39

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