If possible, choose k so that the following function is continuous on any interval:

f (x) = (5x^4-20x^3) / (x-4), x≠4

f (x) = K, x=4

k=?,

We need to cancel out the discontinuity in x = 4

In order to do that, factorize the numerator:

5x⁴ - 20x³ = 5x³ (x-4)

This way, your function will be:

f (x) = 5x³ (x-4) / (x-4)

and the two parentheses cancel out, leaving

f (x) = 5x³

which at x = 4 gives:

f (4) = 5·4³ = 5 · 64 = 320

Therefore K = 320.