Derivates given the value of a

[YummyBacon]

I've been searching for help all across the internet. My teacher isn't avaible and neither does he even teach me anything, I have to rely on youtube videos to learn new information. I've attempted to solve this problem, but my work keeps ending up confusing and messy. I would really appreicate if someone could solve and explain this question for me. Thank you.

 

[tkhunny]

a) What's the definition? Write it out.
b) What's the alternate definition? Write it out.
c) What's f(3)? You'll need that.

See: https://tutorial.math.lamar.edu/Classes/CalcI/DefnOfDerivative.aspx

 

[Harry_the_cat]

Let's see what you have done so far so we can work out how to help.

 

[YummyBacon]

Let's see what you have done so far so we can work out how to help.

For the first question, I inserted the proper numbers into the equation and then multiplied by the conjugate. I did a bit of algebra and then my answer was 1/4. I attempted to do something similar for 4b, but I got some weird number. I'm pretty sure I'm supposed to get the same answer for both questions, right? I probably made a slight error, my work looks sloppy.

 

[Harry_the_cat]

1/4 is the correct answer. Check your working for 4b.